Math 146 - Calculus II for the Life and Environmental Sciences

Credits: 4

Course Description: The course is the second in the sequence of calculus courses for life science and environmental science majors. The topics covered in this course do not parallel the topics covered in the Math 141: Calculus II sections; however, the material covered in this course introduces the student to mathematical fields that are commonly applied in the study of life and environmental sciences. Applications presented in this course have origins in biological and environmental systems. The course begins with a brief review of integration techniques learned in Calculus I, and continues with a thorough analysis of integration. Computational methods, differential equations, linear algebra and multivariable calculus are introduced so that the student may examine dynamical systems that are central to understanding the behavior of many physical models.

Pre-Requisites: MATH 140 or MATH 145.

This course does not fulfill the Calculus II (Math 141) requirement and does not serve as a prerequisite for Multivariable Calculus (Math 240). This course satisfies the following GenEd requirements: Quantitative Reasoning, Distribution II: MT.

Frequency: Offered every Spring semester.

Current Textbook: Neuhauser, C., Calculus for Biology and Medicine, 2nd ed., Pearson Education Check with your instructor to make sure this is the textbook used for your section.

Chapter 7: Integration Techniques and Computational Methods

1. The substitution rule
2. Integration by parts
3. Practicing integration and partial fractions
4. Improper integrals
5. Numerical integration
6. Tables of integrals
7. Taylor Approximation

Chapter 8: Differential Equations

1. Solving differential equations
2. Equilibria and their stability
3. Systems of autonomous equaltions

Chapter 9: Linear Algebra and Analytic Geometry

1. Linear systems
2. Matrices
3. Linear maps, eigenvectors and eigenvalues
4. Analytic geometry

Chapter 10: Multivariable Calculus

• 10.1 Functions of two or more independent variables
• 10.2 Limits and continuity
• 10.3 Partial derivatives
• 10.4 Tangent planes, differentiability and linearization
• 10.7 Systems of difference equations

Chapter 11: Systems of Differential Equations

1. Linear systems: theory
2. Linear systems: applications
3. Nonlinear autonomous systems: theory
4. Nonlinear systems: applications

The order of presentation of the contents of this syllabus, exams, and grading policies are entirely at the discretion of the individual instructor.