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;