AMS 510, Analytic Methods for Applied Mathematics and Statistics 

Review of techniques of multivariate calculus, convergence and limits, matrix analysis, vector space basics, and Lagrange multipliers. 
3 credits, ABCF grading 

Required Textbooks for Fall 2024 Semester:

"Linear Algebra and Its Applications" by Gilbert Strang; Brooks/Cole; ISBN# 9780030105678

"Advanced Calculus: Theory and Practice", by John Srdjan Petrovic; CRC Press LLC; ISBN# 9781466565630

Additionally, lecture notes will be provided by the instructor

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(Past Course Materials):

Recommended Textbooks for Fall 2023 Semester:

"How to Prove It: A Structured Approach" by Daniel J. Velleman; Cambridge University Press; ISBN# 9780521675994

"Introduction to Linear Algebra" by Gilbert Strang, 5th edition, 2016, Wellesley-Cambridge Press; ISBN: 9780098023276

"Calculus" by Ron Larson & Bruce Edwards, 11th edition, 2017, Cengage Learning; ISBN: 9781337275347

 

 

AMS 510 Instructor Page

Learning Outcomes:

1.) Demonstrate mastery of topics in linear algebra:
        * Review fundamentals of linear algebra, Cauchy Schwarz;
        * Echelon form, pivot and free variables, existence and uniqueness;
        * Linear independence, basis, space and dimension;
        * Homogegeous and nonhomogeneous equations, column and null spaces;
        * Linear mapping, kernel and range.

2.) Demonstrate mastery of differentiation in calculus:
        * Function, limit, continuity and derivative;
        * Product rule, quotient rule, and chain rule
        * Mean value theorem and L'Hospital's rule;
        * Maximum and minimum.

3.) Demonstrate mastery of integration in calculus:
        * Antiderivative, Riemann sum and Newton-Leibniz formula;
        * Integration techniques: substitution method, integration by part, partial fraction;
        * Area and volume by revolution, improper integral.

4.) Demonstrate mastery of multivariable calculus:
        * Multivariable function, limit, and partial derivatives;
        * Transformation, Jacobian, and Lagrangian multiplier;
        * Double and triple integrals;
        * Applications, volume, mass, moment of inertial;
        * Transformation to polar, cylindrical and spherical coordinates;

5.) Advanced topics (if time allows):
        * Vector functions, gradient, divergence and curl;
        * Surface and line integrals;
        * Green's theorem and Stokes theorem;