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# MATH 146 : Calculus II for 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.

Comments: 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.

 Topics: Chapter 7: Integration Techniques and Computational Methods The substitution rule Integration by parts Practicing integration and partial fractions Improper integrals Numerical integration Tables of integrals Taylor Approximation Chapter 8: Differential Equations Solving differential equations Equilibria and their stability Systems of autonomous equaltions Chapter 9: Linear Algebra and Analytic Geometry Linear systems Matrices Linear maps, eigenvectors and eigenvalues 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 Linear systems: theory Linear systems: applications Nonlinear autonomous systems: theory Nonlinear systems: applications

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