AMS 161, Applied Calculus II
Catalog Description: Analytic and numerical methods of integration; interpretations and applications
of integration; differential equations models and elementary solution techniques;
phase planes; Taylor series and Fourier series. Intended for CEAS majors. Not for
credit in addition to MAT 127 or 132.
Prerequisites: AMS 151 or MAT 131 or MAT 126.
3 credits
WebAssign for Stewart/Kokoska's "Calculus: Concepts & Contexts", 5e Single-Term Instant Access 9780357748978
Topics
1. Concepts on Integration and Methods of Integration: substitution, integration by
parts, volume problems, approximating integrals with Riemann sums, improper integrals
- 10 hours
2. Applications of the Integral: volume and other geometric applications, parametric
curves, arc lengths; probability; economic interpretations - 6 hours
3. Elements of Differential Equations: slope fields, Euler's method, applications
and modeling - 7 hours
4. Systems of first-order differential equations and second-order differential equations,
including solutions involving complex numbers - 8 hours.
5. A pproximations and series: Taylor series, Fourier polynomials - 5 hours
6. Review and Tests - 6 hours
Learning Outcomes for AMS 161, Applied Calculus II
1.) Demonstrate a conceptual understanding of the Fundamental Theorem of Calculus
and its technical application to evaluate definite and indefinite integrals.
* Solve problems graphically and analytically that illustrate how integration
and differentiation are inverse operations;
* Use the Fundamental Theorem of Calculus to evaluate definite integrals whose
limits are functions of x.
2.) Demonstrate skill in integrating basic mathematical functions, such as:
* polynomials,
* exponential functions
* sine and cosine functions.
3.) Develop facility with important integration tools such as:
* reverse chain rule;
* substitution methods;
* integration by parts;
* tables of integrals.
4.) Solve problems involving geometric applications of integration:
* area problems;
* volume problems;
* arclength problems
5.) Develop basic skills with using numerical methods to evaluate integrals
* right-hand, left-hand, and trapezoidal rules;
* Simpson’s rule.
6.) Solve problems involving applications of integration to in physics and economics.
* center of mass problems;
* force problems;
* work problems;
* present value of multi-year investments.
7.) Solve problems with sequences and series, including:
* find limits of sequences;
* test series for convergence;
* sum series.
8.) Demonstrate facility with constructing and using Taylor and Fourier series.
* Taylor series for simple functions
* Taylor series for composite functions and products of functions;
* Taylor series to integration problems;
* simple Fourier series.
9.) Model problems with simple types of differential equations and solve these problems:
* model problems with solve first-order linear differential equations and solve
them;
* use separation of variables to solve rate problems such as Newton’s law of
cooling and logistic equations;
* solve second-order linear differential equations.