Week 4: Geometric interpretation of differentiability, Chain rule, Taylor’s theorem. Maxima and Minima
Course Material
- Week 1:The Riemann-Stieltjes Integrals: Definition and existence of integrals, Properties of integrals
- Week 2: Real Valued Functions of Several Variables
- Week 3: Continuous real valued functions, Partial derivatives and differentials
- Week 4: Geometric interpretation of differentiability, Chain rule, Taylor’s theorem. Maxima and Minima
- Week 5: Vector Valued Functions of Several Variables Linear transformations and matrices
- Week 6: Continuous and differentiable transformations, Chain rule for transformations
- Week 7: Inverse function theorem, Implicit function theorem, Jacobians, Method of Lagrange multipliers
- Week 8: Functions of Bounded Variation: Definition and examples, properties of functions of bounded variation
- Week 9: Mid Term Examination
- Week 10: Improper Integrals: Types of improper integrals
- Week 11: Tests for convergence of improper integrals
- Week 12: Absolute and conditional convergence of improper integrals
- Week 13: Sequences and Series of Functions: Power series
- Week 14: Definition of point-wise and uniform convergence
- Week 15: Uniform convergence and continuity
- Week 16: Uniform convergence and differentiation
- Week 17: Examples of uniform convergence
- Week 18: Final Term Examination
- Chapters 18
- Department Mathematics
- Teacher
Dr. Muhammad Samraiz
