College of Engineering

Chemical and Biological Engineering

Study Abroad in Chemical Engineering
Chemical and Biological Engineering Curriculum
Curriculum Modification for CBE
Facilities
Courses

2014 Engineering Hall, 1415 Engineering Drive, Madison, WI 53706; 608/262-1092; fax 608/262-5434; www.engr.wisc.edu/che

Professors Abbott, de Pablo, Dumesic, Graham (chair), Klingenberg, Kuech, Murphy, Nealey, Rawlings, Yin; Associate Professors Mavrikakis, Palecek, Root, Swaney; Assistant Professors Lynn, Maravelias, Shusta; Emeritus Professors Bird, Chapman, Duffie, Hill, Langer, Lightfoot, Ray, Rudd, Sather

Chemical engineers exploit advances in chemistry and biology to create new products, design chemical processes, develop energy resources, and protect the environment. Students receive a thorough grounding in chemistry, biology, mathematics and physics. With this broad scientific training, chemical engineers work effectively on a diverse set of problems involving chemical, physical, and biological phenomena. For example, chemical engineers develop environmentally benign and safe processes to make the chemical products that people depend on. They work in research and development laboratories, creating polymeric materials with improved performance and durability. They work in manufacturing, making vaccines and antibiotics. They invent new ways to keep our food and water supplies safe. Opportunities for chemical engineers span numerous industries: pharmaceuticals, polymers, energy, food, consumer products, biotechnology, and electronic and optical materials. Graduates understand the needs of society, and use their training in science and technology to meet those needs.

The chemical engineering program develops the student's capability for invention and analysis of chemical processes and products. Students in the program take several classes in chemistry, along with courses in physics, mathematics, and biology. The curriculum provides a rigorous education in the fundamental chemical engineering sciences of thermodynamics, transport phenomena, and kinetics, as well as more applied areas such as materials science, biochemical engineering, or chemical process design. Because engineers must be skilled communicators, the curriculum places considerable emphasis on technical report writing, team projects, and formal and informal oral presentation. In addition, students broaden their understanding of people and society by taking several courses in the humanities and social sciences.

The B.S. program in chemical engineering leads to a wide variety of careers. Graduates are prepared for professional lives in industry, government, engineering design, or consulting companies. Graduates with a more practical, hands-on approach are employed in manufacturing support, process development, product development, design, construction, or technical sales. They rapidly advance to responsible technical supervisory and management positions. Graduates with a research interest work to improve understanding of scientific engineering principles, and to apply these principles to solve emerging problems. Entrepreneurial graduates work in smaller enterprises, or create their own businesses, developing the major industries of tomorrow. An undergraduate degree in chemical engineering provides a strong basis for advanced study in graduate school, or for further training in medicine, law, or policy.

Study Abroad in Chemical Engineering

Return to Top

Chemical engineering students have several options to participate in engineering study programs in universities and engineering schools outside the United States. Present programs include study in Austria, Denmark, France, Germany, Hungary, Japan, Mexico, Puerto Rico, Spain, and the United Kingdom. Other placements can be arranged. In these programs course credits may be earned to fulfill certain chemical engineering degree requirements. Contact Marianne Bird Bear, M1002a Engineering Centers Building, for further information.

Chemical and Biological Engineering Curriculum

Return to Top

The following curriculum applies to students admitted to the chemical engineering degree program.

Summary of Requirements

Mathematics Requirement, 19 cr
Computer Science Requirement, 3 cr
Science Requirement, 37 cr
Core Engineering Requirement, 50 cr
Communications Skills, Part A, Requirement, 2 cr
Liberal Studies Requirement, 16 cr
Free Electives, 6 cr

Total Credits: 133

I. Mathematics Requirement, 19 credits

Math 221 Calculus and Analytic Geometry, 5 cr
Math 222 Calculus and Analytic Geometry, 5 cr
Math 234 Calculus— Functions of Several Variables, 3 cr
Math 319 Techniques in Ordinary Differential Equations or Math 320 Linear Mathematics, 3 cr
Statistics 324 Introductory Applied Statistics for Engineers, 3 cr

Transfer students must have equivalent math courses to meet the calculus requirement with a minimum of 12 credits to cover the three-course basic math sequence. Any deficiency in total math credits must be made up with electives in science or engineering.

II. Computer Science Requirement, 3 credits

Comp Sci 310 Problem Solving Using Computers, 3 cr

III. Science Requirement, 37 credits
A. Basic Science, 19 credits

Chem 109 General and Analytical Chemistry I, 5 cr
Chem 329 Fundamentals of Analytical Science, 4 cr
Physics 201 or 207 General Physics, 5 cr
Physics 202 or 208 General Physics, 5 cr

Transfer students whose general chemistry courses do not contain significant analytical chemistry content must take Chemistry 223 (or Chemistry 221) for their chemistry laboratory elective. Credit shortages caused by transfer of freshman chemistry courses at fewer than 10 credits must be made up with chemistry, biochemistry, or chemical engineering courses. Transfer students who receive fewer than 6 credits for Physics 201/202 or 207/208 courses must make up the credit shortage with another Physics course.

Life Science, 6 cr
Biochem 501 Introduction to Biochemistry, 3 cr
Zool 570 Cellular Biology, 3 cr
Biocore 301 and 303 may be used to satisfy the Life Science requirement

B. Advanced Chemistry, 12 credits

Chem 343 Introductory Organic Chemistry, 3 cr
Chem 344 Introductory Organic Chemistry Lab, 2 cr
Chem 345 Intermediate Organic Chemistry, 3 cr
Chem 562 Physical Chemistry, 3 cr
Chem 563 Physical Chemistry Lab, 1 cr

Both the chemistry lab elective and the advanced chemistry elective must be chosen from lists of approved courses in the CBE Curriculum Guide available at the chemical and biological engineering department.

IV. Core Engineering Requirement, 50 credits

CBE 250 Process Synthesis, 3 cr
CBE 211 Chemical Process Thermodynamics, 3 cr
CBE 311 Thermodynamics of Mixtures, 3 cr
CBE 320 Introductory Transport Phenomena, 4 cr
CBE 324 Transport Phenomena Lab, 2 cr
CBE 326 Momentum and Heat Transfer Operations, 3 cr
CBE 424 Operations and Process Laboratory, 5 cr
CBE 426 Mass Transfer Operations, 3 cr
CBE 430 Chemical Kinetics and Reactor Design, 3 cr
CBE 440 Chemical Engineering Materials, 3 cr, or
CBE 540 Polymer Science and Technology, 3 cr
CBE 450 Process Design, 3 cr
CBE 470 Process Dynamics and Control, 3 cr
ECE 376 Electrical and Electronic Circuits, 3 cr
CBE Electives, 6 cr Engineering Elective, 3 cr

Chemical engineering electives may be chosen from any of the chemical engineering courses that are not required, with the exception of CBE 425. A maximum of 2 credits of co-op work (CBE 001) may be applied to meet the CBE elective requirement. Qualified undergraduates may take graduate-level (600 or 700) courses to fulfill this requirement.

Engineering elective courses are to be selected from the College of Engineering (preferably outside chemical engineering). At least 1 of the 3 credits must be obtained from a list of approved courses in the CBE Curriculum Guide, that carry engineering topics credits.

A maximum of 6 credits of CBE 599 and/or CBE 699 may be used to satisfy the 9-credit sequence of CBE and Engineering elective courses.

V. Communications Skills Requirement, 2 credits

For Part A of the General Education Communication Requirement (2 cr) students must select one course with an "a" designation in "g" of the "geBLC" column of the Timetable, such as the following: Ag Jour 100, Com Arts 100, EPD 155, English 100, ILS 200, or Family Comm 100. English 118 is also approved for those students required to study English as a second language. Some students will be exempt from this requirement based on their placement test scores or advanced placement in English.

CBE 424 satisfies Part B of the General Education Communication Skills Requirement.

VI. Liberal Studies Requirement, 16 credits
  1. Liberal studies elective courses must be classified as either Humanities, Social Studies, or Literature courses (identified by the letters H, S, L, or Z in "B" of the "geBLC" column of the Timetable). At least 6 credits must have a breadth designation of Humanities (H, L, or Z), and at least 3 credits must have a designation of Social Studies (S or Z). Foreign language courses count as H credits.
  2. Among the liberal studies electives 9-12 credits must be chosen to form a concentration in one field or two closely related fields, and at least one of the courses in the concentration must be at an Intermediate or Advanced level (indicated by an I, A, or D in the L column of the "geBLC" column of the Timetable).
  3. A minimum of 4 credits must be outside the field of concentration.
  4. A 3-credit ethnic studies course must be selected from the College of Letters and Science. Acceptable courses are identified by the letter "e" in the "geBLC" column of the Timetable. If appropriate, the ethnic studies course may be among those used to satisfy the concentration requirement.
  5. Retroactive credits may be awarded for foreign-language work done in high school. The following conditions apply:
    1. A university-level foreign language course must be taken before the student has earned 30 college credits in residence;
    2. Retroactive Language Credit Request Form must be completed and submitted to the language instructor during the first two weeks of class;
    3. The student must earn a B or better in this course (or a C or better if it is German).
      Such credits do not count toward the 16 liberal-studies credits required. They may, however, be used to satisfy the concentration and depth requirements stated in item 2 above and count as degree credits.
  6. English composition courses, English as a Second Language Courses, and basic communications arts courses are not accepted as liberal studies electives.
VII. Free Electives, 6 credits

Students who satisfy the Communications Part A requirement by examination will have an additional 2 credits of free electives. Transfer students who receive fewer transfer credits for a required course than are given for the same course on the Madison campus must increase their free elective credits to meet the minimum 133 total credit requirement for the chemical engineering degree.

VIII. General College of Engineering Requirements

Engineering students must complete several General College Requirements (GCR: see http://studentsservices.engr.wisc.edu/current) before admission to a degree-granting program. As part of the GCR, students must take courses in five categories (communications, physics, chemistry, introduction to engineering, and mathematics). Each of these courses can also be used to satisfy one of the requirements listed in items I-VII above. While various courses can be selected in these categories, students who wish to be admitted to chemical engineering are strongly encouraged to take the specific courses listed below.

General College Requirements
  1. Comm A
  2. Physics
  3. Chemistry
  4. Introduction to Engineering
  5. Mathematics
Recommended Courses
  1. EPD 155 (2 cr) (any Comm A course maybe taken)
  2. Phys 201 (5 cr) (EMA 201 (3 cr) + EMA 202 (3 cr) maybe substituted for Phys 201
  3. Chem 109 (5 cr) (Chem 103 (4 cr) + Chem 104 (5 cr) maybe substituted for Chem 109
  4. EPD 101 (2 cr) or EPD 160 (3 cr) (EPD 101 can count toward the department free elective or liberal elective requirements; EPD 160 can count toward the department free elective requirement. Intro to Engineering approved by GCR can count toward the free elective requirements
  5. Math 221 (5 cr) and Math 222 (5 cr) (Math 217 (5 cr) maybe substituted for Math 221; Math 275 (5 cr) + Math 276 (5 cr) maybe substituted for Math 221 + Math 222. These recommended courses present the preferred topics at a level suitable for chemical engineering Students. Other alternatives that satisfy the General College Requirements will be accepted for admission into the chemical engineering degree program, but these choices may reduce the number of free electives available in the curriculum.
Recommended Course Sequence

Note: Students who are majoring in programs that require chemistry course work should check with an academic advisor to obtain the most current information.

Freshman Year, First Semester, 14-15 credits

Chem 109 General and Analytical Chemistry, 5 cr
Math 221 Calculus and Analytic Geometry, 5 cr
Communications Skills Elective, 2 cr
Introduction to Engineering, 2-3 cr

Second Semester, 17 credits

Chem 329 Fundamentals of Analytical Chemistry, 5 cr
Math 222 Calculus and Analytic Geometry, 5 cr
Physics 201 General Physics, 5 cr
Liberal Studies Elective 3 cr.

Sophomore Year, First Semester, 17 credits

CBE 250 Process Synthesis, 3 cr
Chem 343 Introductory Organic Chemistry, 3 cr
Math 234 Calculus— Functions of Several Variables, 3 cr
Physics 202 General Physics, 5 cr
Comp Sci 310 Problem Solving Using Computers, 3 cr

Second Semester, 17 credits

CBE 211 Chemical Process Thermodynamics, 3 cr
Chem 344 Introductory Organic Chemistry Lab, 2 cr
Chem 345 Intermediate Organic Chemistry, 3 cr
Math 319 or 320, 3 cr
Stats 324 Intro Applied Stats for Engineers, 3 cr
Biochem 501 Intro to Biochemistry, 3 cr

Junior Year, First Semester, 17 credits

CBE 311 Thermodynamics of Mixtures, 3 cr
CBE 320 Introductory Transport Phenomena, 4 cr
ECE 376 Electrical and Electronic Circuits, 3 cr
Chem 563 Physical Chemistry Lab, 1 cr
Zoology 570 Cell Biology, 3 cr
Liberal Studies Elective, 3 cr

Second Semester, 15-16 credits

CBE 324 Transport Phenomena Lab, 2 cr
CBE 326 Momentum and Heat Transfer Operations, 3 cr
Chem 562 Physical Chemistry, 3 cr
Liberal Studies Elective, 4-5 cr
Engineering Elective, 3 cr
Depending on choice for the Introduction to Engineering course selected in the freshman year.

Senior Year, First Semester, 15 credits

CBE 426 Mass Transfer Operations, 3 cr
CBE 430 Chemical Kinetics and Reactor Design, 3 cr
CBE Elective, 3 cr
CBE 440 Chemical Engineering Materials, 3 cr
or CBE 540 Polymer Science & Technology, 3 cr
Liberal Studies Elective, 3 cr

Second Semester, 15 credits

CBE 450 Process Design, 3 cr
CBE 470 Process Dynamics and Control, 3 cr
CBE Elective, 3 cr
Free Elective, 6 cr

Senior Year, Summer Session, 5 credits

CBE 424 Operations and Process Lab, 5 cr

Total credits for graduation: 133
Course Substitution Regulations
  1. Any student may, with advisor approval, replace up to 12 credits of required courses in the curriculum, except CBE 424, by an equal number of credits of other courses within the limitations listed under (3) below.
  2. Any student who wishes to amend the curriculum by more than 12 credits or wishes to appeal the advisor's decision in (1) or to request exception to (3) below must submit a written request to the chair of the department, who will bring it to the department faculty for consideration.
  3. Restrictions on course substitutions are as follows: a. Physics course may be replaced by science or engineering courses;
  4. Chemistry/life courses must be replaced by courses with significant chemistry/life content;
  5. Engineering courses must be replaced by engineering courses;
  6. Lab courses must be replaced by courses with an equal number of hours of lab courses;
  7. English 101, English as a second language courses, and Math 112-114 may not be used for course substitutions.

Curriculum Modification for CBE

Return to Top

Students wishing to specialize or to prepare for graduate study in technical or nontechnical areas may use electives and the course substitution regulations to achieve a curriculum that will enhance professional development in a particular specialty. Examples for several technical areas are listed below. Others can be found on the chemical engineering Web site at www.engr.wisc.edu/che. Several options are provided for selecting particular electives. Students interested in preparing for graduate studies in nontechnical areas should also consult with their advisor.

Bioprocess Engineering

CBE 440/540;
CBE 540 CBE elective: BSE 542, 642
Free electives: Genetics 466, Food Sci 550

Biomedical and Premedical

CBE 440/540: CBE 540
CBE elective: CBE 560
Engineering elective: BME 314, 401, 410, 430

Environmental and Energy

CBE 440/450: CBE 440
CBE elective: CBE 567, 535
Engineering elective: CEE 320, 326, 521, 522
Free elective: Envir St. 343, Geol 411

Polymers

CBE 440/540: CBE 440
CBE elective: CBE 540, 541, 525
Engineering elective: ME 417, 418

Process Systems and Technology Management

Engineering elective: IE 313, 433, CS 412, 513 Free elective: Math 340, 415

Food Engineering

CBE 440/550: CBE 440
CBE elective: CBE 540, 565
Engineering electives: CEE 521, 320, BSE 642
Free elective: Food Sci 410

Solid State Materials

CBE 440/450: CBE 440
CBE elective: CBE 544
Engineering electives: MSE 448, 570, ECE 335, 466
Free elective: Physics 531, 551

Facilities

Return to Top

Facilities available for instruction and research include: Biochemical Process Lab Electrochemistry Lab Plastics Lab Process Dynamics and Control Lab Research Labs Transport Phenomena Lab Unit Operations Lab

Courses

Return to Top

1 Cooperative Education Program. I, II, SS; 1 cr. Work experience which combines classroom theory with practical knowledge of operations to provide students with a background upon which to base a professional career. P: So st.

211 Chemical Process Thermodynamics. I, II; 3 cr. Introduction to thermodynamics, energy balances, applications to steady state and unsteady state processes, behavior of pure fluids, chemical reaction equilibria. P: Math 234, Physics 201 or equiv; Comp Sci 310 or equiv or con reg; CBE 250 with grade of C or better.

250 Process Synthesis. I, II; 3 cr (P-E). An introduction to the invention of processes for the large scale, low cost processing of materials such as water, chemicals, petroleum products, food, drugs and wastes. Open to students in any field. P: Chem 329 or con reg.

311 Thermodynamics of Mixtures. I, II; 3 cr. Properties of ideal and non-ideal vapors and liquids, ideal and non-ideal multicomponent vapor-liquid and liquid-liquid equilibria, complex chemical reaction equilibria, electrolytic solutions, surface thermodynamics, solid phase thermodynamics. P: CBE 211 with grade of C or better.

320 Introductory Transport Phenomena. (Crosslisted with BME) I, II; 4 cr (P-I). Mass, momentum, and energy transport; calculation of transport coefficients; solution to problems in viscous flow, heat conduction, and diffusion; dimensional analysis; mass, momentum, and heat transfer coefficients; over-all balances; elementary applications. P: Physics 201, Math 319 or 320, CBE 250 with grade of C or better; or cons inst.

324 Transport Phenomena Lab. I, II; 2 cr (P-I). Determination of thermodynamic properties, transport properties, and transfer coefficients; study of related phenomena. P: CBE 211 & 320, or con reg; Stat 324.

326 Momentum and Heat Transfer Operations. I, II; 3 cr (P-I). Analysis of chemical engineering operations involving fluid flow and heat transfer. Flow of fluids through ducts and porous media; motion of particulate matter in fluids; general design and operation of fluid-flow equipment. Conductive, convective and radiative heat exchange with and without phase change; general design and operation of heat-exchange equipment. P: CBE 211 & 320 with grades of C or better.

424 Operations and Process Laboratory. SS; 5 cr (b-P-A). Experiments in unit operations, and supervised individual assignments selected from areas such as: fluid dynamics, analytical methods, reaction kinetics, plastics technology, and use of computers in data processing and simulation. P: CBE 324, 326, 426 & 430; or cons inst.

425 Undergraduate Rheology Seminar. (Crosslisted with Chem, EMA, ME) I, II; 0-1 cr (A). Rheology seminar course encouraged for all interested in professions related to polymers, suspensions or rheology; will not count toward credit requirement of the major. P: Cons inst or Jr st.

426 Mass Transfer Operations. I, II; 3 cr (P-I). Analysis of chemical engineering operations involving mass transfer. Differential and stagewise separation processes; simultaneous heat and mass transfer; mass transfer accompanied by chemical reaction; general design and operation of mass-transfer equipment. P: CBE 311 & 320 with grades of C or better, or cons inst.

430 Chemical Kinetics and Reactor Design. I, II; 3 cr (P-I). Analysis and interpretation of kinetic data and catalytic phenomena; application of basic engineering principles to chemical reactor design. P: CBE 311 & 320; or cons inst.

440 Chemical Engineering Materials. I, II; 3 cr (P-I). Structure and properties of metallic and nonmetallic materials of construction; interrelations between chemical bonding, structure, and behavior of materials. P: Chem 345.

450 Process Design. I, II; 3 cr (A). Analysis and design of chemical processing systems and equipment. P: CBE 326, 426 & 430 or cons inst.

470 Process Dynamics and Control. I, II; 3 cr (A). A systematic introduction to dynamic behavior and automatic control of industrial processes; lab includes instrumentation, measurement and control of process variables by using conventional hardware and real-time digital computers. P: CBE 326 & ECE 376; CBE 430 or con reg.

510 Introduction to Tissue Engineering. (Crosslisted with BME) I; 3 cr. Overview of tissue engineering, including discussion of cell sources, cell-material interactions, tailoring biomaterials, methods of culture and characterization of engineering tissues, ethical issues, concluding with case studies of specific types of tissue engineering. Optional laboratory exercises offered throughout semester. P: BME 430 or equiv, or cons inst.

517 Biology in Engineering Seminar. (Crosslisted with BME, BSE) I; 1 cr. Current topics at the interface of biology and engineering with special emphasis on the ways in which engineers have contributed to knowledge and advances in biology. P: Jr st in engr & one college-level biol crse.

520 Stem Cell Bioengineering. (Crosslisted with BME) I; 3 cr. Covers engineering approaches that are used to understand and manipulate stem cells. Concepts covered include: introduction to stem cell biology, quantitative modeling of stem cell signaling, methods to engineer the stem cell microenvironment, and the role of stem cells in tissue development and regeneration. P: Math 319 or 320, Zoology 470 or 570, Chem 343, or cons inst.

525 Macromolecular Hydrodynamics. (Crosslisted with ME) Irr.; 3 cr (P-A). Observed phenomena in polymeric flow systems. Techniques of viscometry and viscoelastic measurements for polymeric fluids. Rheological models. Analytical solutions to flow problems: non-Newtonian viscosity, linear viscoelasticity, normal stresses, recoil, stress relaxation, etc. Dimensional analysis. Unit operations of the polymer industry: extrusion, blow molding, injection molding, mixing. P: CBE 320 or ME 363 or equiv or cons inst.

535 Heterogeneous Catalysis: Principles and Applications. II; 3 cr. This course discusses catalytic phenomena, with extensions to reactor design and catalyst characterization. Examples will be drawn from current problems in catalysis. P: CBE 430 or cons inst.

540 Polymer Science and Technology. I, II; 3 cr (P-A). Synthesis, properties, and fabrication of plastic materials of industrial importance. P: Chem 345; CBE 326 & 430, or con reg; Stat 324; or cons inst.

541 Plastics and High Polymer Laboratory. Irr.; 1-3 cr (P-A). Experiments on polymerization, fabrication, and testing of plastics. P: CBE 540 or con reg; or Chem 664 or con reg.

544 Processing of Electronic Materials. (Crosslisted with ECE, MS&E) Irr.; 3 cr (I). Physics and chemistry principles underlying microelectronic materials processing. Effects of processing on materials and structures important in microelectronic and opto-electronic devices. P: CBE 440 or MS&E 351 or ECE 335; or cons inst.

547 Introduction to Colloid and Interface Science. I; 3 cr. Introduction to topics in colloid and interface science. Topics include: sedimentation and diffusion, solution thermodynamics, rheology, light scattering, surface tension and contact angle, adsorption, association colloids, particle interactions, electrokinetics, and colloidal stability. P: Chem 561 or 562 or equiv, or cons inst.

555 Seminar—Chemical Engineering Connections. I, II; 1 cr. Considers a variety of current engineering applications and problems. Students will investigate background information on topics of their choice, and present seminars to describe how engineering fundamentals interact with societal impact and how our undergraduate education in chemical engineering is relevant to societal concerns at large. P: Sr st or cons inst.

560 Biochemical Engineering. (Crosslisted with BME) I; 3 cr (P-A). Application of chemical engineering principles to biomedical and microbiological problems. P: CBE 426; Chem 561 or 562; Biochem 501 or equiv; or cons inst.

561 Biomolecular Engineering Laboratory. (Crosslisted with BME) Irr.; 3 cr. Brief review of physical chemistry of biological macromolecules. Theory and laboratory experiments aimed at developing skills at preparing and characterizing biological macromolecules and macromolecular assemblies. Half-semester-long laboratory project focused on design of a specific process/product involving biomolecules. P: CBE 311; Chem 561 or 562 or 565 or equiv; Biocore 303 or Biochem 501 or equiv; or cons inst.

562 Special Topics in Chemical Engineering. I, II; 1-3 cr. Topics of specialized interest to majors in chemical engineering. Given on demand. P: Jr st and cons inst.

565 Food Process Engineering. (Crosslisted with Food Sci) II; 3 cr. Application of engineering principles to the quantitative analysis of food processing systems. Physical/chemical characteristics of biological systems, flow processes, preservation processes and separation processes. P: CBE 326 & 426; Chem 345.

567 Solar Energy Technology. (Crosslisted with ME) I; 3 cr (A). Radiant energy transfer and its application to solar exchangers; energy balances for solar exchangers, review of theory, economics, and practice of solar energy applications. P: ME 364 or CBE 326 or cons inst.

599 Special Problems. I, II, SS; 1-4 cr (A). Research or independent study.

620 Intermediate Transport Phenomena. I; 3 cr (A). Mass, momentum, and energy transport; kinetic theory of transport properties; analytical and approximate solutions to the equations of change; boundary layer theory; turbulence; simultaneous heat and mass transfer; multicomponent diffusion. P: Grad st in CBE or cons inst.

660 Intermediate Problems in Chemical Engineering. I; 3 cr. Illustrations of solving chemical engineering problems by using a variety of mathematical topics such as ordinary and partial differential equations, Laplace transform, Bessel functions, matrices, and tensor analysis. Problem formulation and interpretation of results emphasized. P: Grad st in CBE or cons inst.

699 Advanced Independent Studies. I, II, SS; 1-5 cr (A). Research on assigned topics.