Syllabus
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Course Code: B-MAT 201 Course Name: Advanced Calculus |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Mean value theorems: Rolle’s Theorem and Lagrange’s mean value theorem and their geometrical interpretations, Cauchy mean value theorem. Taylor’s Theorem with various forms of remainders, Darboux intermediate value theorem for derivatives. Indeterminate forms. | |
| 2 | Functions of several variables, Level curves and surfaces, Limits and continuity. Partial differentiation. Total Differentials; Composite functions & implicit functions. Chain rule. Change of variables. Homogenous functions & Euler’s theorem on homogeneous functions. Taylor’s theorem for functions of two or more variables. | |
| 3 | Differentiability of real valued functions of two variables. Schwarz and Young’s theorem. Implicit function theorem. Extrema of functions of two and more variables; Maxima, Minima critical points, Method of Lagrange multipliers. Constrained optimization problems | |
| 4 | Double integration over rectangular and nonrectangular regions, Double integrals in polar coordinates. Jacobian. Change of order of integration. Triple integral over a parallelepiped and solid regions, Volume by triple integrals, Triple integration in cylindrical and spherical coordinates. Dirichlet integrals. Beta and Gamma functions. | |
