MATH 2412

Calculus II for Life Sciences Summer (III) 2011

Instructor: Jeong-Mi Yoon, Ph.D., S712, x 8457, yoonj@uhd.edu.

Time & Place: MTWR 12:30pm - 3:15pm in A607 (CRN # 40060).

Office Hours: MTWR 3:30-4:30 pm or by Appointments.

Course Webpage: http://cms.dt.uh.edu/Faculty/YoonJ/course.htm

Textbook: Calculus for Biology and Medicine, 3rd edition by C. Neuhauser, Pearson (2011), ISBN 978-0-321-64468-8.

Prerequisites: A grade of C or better in Math 2411 (Calculus for Life Sciences I) OR Math 2401 (Calculus I).

Catalog Description: This course is a continuation of Math 2411 (Calculus for Life Sciences I). The topics include integration, approximation by Taylor series, differential equations, matrices, eigenvalues and eigenvectors, functions of several variables, partial derivatives, tangent planes and linearization, systems of difference equations, systems of linear and nonlinear differential equations, and equilibria and stability.

Course Goals: At the completion of the course, the student should be able to:

1. Differentiate and integrate transcendental functions and equations expressed in polar coordinates.

2. Evaluate integrals by using the various elementary methods of integration, which include substitution, trigonometric substitution, integration by parts.

3. Evaluate improper integrals.

4. Discuss the equilibria and stability of linear systems of differential equations.

4. Discuss the existence and uniqueness of solutions of a system of linear equations.

5. Evaluate the determinant of a matrix and perform computations using the basic properties of the determinant.

6. Compute the eigenvalues and the corresponding eigenvectors of square matrices.

7. Discuss linear systems of ordinary differential equations and nonlinear systems of ordinary differential equations analytically and numerically. The goal of this course is to impart to students the excitement and usefulness of mathematics as a fundamental tool in solving real-world problems. The course emphasizes manners in which mathematical models are constructed for physical problems and illustrates from many fields of endeavor, such as the physical sciences, biology, and traffic dynamics.

Method of Evaluation: Three tests, Final (Comprehensive) exam, and Homework Assignments.

Exam Date: Test I – July 20 (Wednesday) in class,

Test II – July 28 (Thursday) in class,

Test III – August 8 (Monday) a take-home test,

Final – August 10 (Thursday) in class,

Grading Policy: Test @ 20 % each; Final @ 35 %; Homeworks @ 5 %.

THE FINAL EXAM MUST BE TAKEN BY ALL THE STUDENTS. THERE WILL BE NO OTHER MAKE-UP EXAMS!

The Last Day to Withdraw from a course is August 4 (Thursday).

Course Contents:

• Integration by parts (Sec. 7.2)
• Improper integrals (Sec. 7.4)
• Numerical integration and theory (Sec. 7.5)
• Approximation by Taylor series (Sec. 7.7)
• Solving differential equations, Introduction (Sec. 8.1)
• Solving differential equations, Examples and applications (Sec. 8.1)
• Equilibria and stability, Introduction (Sec. 8.2)
• Equilibria and stability, Examples and applications (Sec. 8.2)
• Linear systems (Sec. 9.1)
• Matrices (Sec. 9.2)
• Eigenvalues and eigenvectors, Introduction (Sec. 9.3)
• Eigenvalues and eigenvectors, Examples and applications (Sec. 9.3)
• Elements of analytical geometry (Sec. 9.4)
• Functions of multiple variables, Partial derivatives (Sec. 10.1-3)
• Tangent plane, linearization and differentiability (Sec. 10.4)
• Directional derivatives and gradient vector (Sec. 10.5)
• Maxima and minima (Sec. 10.6)
• Systems of autonomous equations and examples (Sec. 8.3)
• Linear systems of ODEs, Theory (Sec. 11.1)
• Linear systems of ODEs, Examples and applications (Sec. 11.2)
• Nonlinear systems of ODEs, Theory (Sec. 11.3)
• Nonlinear systems of ODEs, Examples and applications (Sec. 11.4)
• Discussion of Applications with Matlab or Maple.

Homework Assignments: Homework will be assigned for each lecture meeting, and it will be collected on every test day. Late homework will not be accepted. The solutions to homework problems will be answered in the next class or office hours by making questions.

UHD Policy: "UHD adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with disabilities. Students with disabilities should register with Disabled Student Services and contact their nstructor(s) in a timely manner to arrange for appropriate accommodations.".