Advanced Calculus For Engineers

About The Course:This course is about basic mathematics, which is a fundamental and essential component of all undergraduate studies in sciences and engineering. This course consists of topics in differential, integral, and vector calculus with applications to various engineering problems. This course will cover calculus of two or more variables in detail. Knowledge of ordinary differential equations are part of this course. Students will learn how to perform double and triple integrals. Topic in vector calculus includesline and surface integrals, Green, Gauss and Stokes theorem. PRE-REQUISITES :Higher SecondaryINTENDED AUDIENCE:All branches of science and engineering

Week 1: Differential calculus of one variable Week 2: Limit, continuity, partial derivatives of functions of two or more variables Week 3: Differentiability of functions of two or more variables Week 4: Differentiation of Homogeneous and Implicit Functions, Taylors theorem of functions of two variables Week 5: Maxima and Minima Week 6: First order ODEs Week 7: Higher order ODEs Week 8: Improper integrals Week 9: Double integrals Week 10: Triple Integrals Week 11: Vector and scalar field, gradient, divergence and curl Week 12: Line and surface integrals. Green, Stokes and Gauss divergence theorems