Week 12: Sigma notation and limits of finite sums, definite integral, the fundamental theorem of calculus
Course Material
- Week 01:Functions and their graphs, Rates of change and tangents to curves
- Week 02:Limit of a function and limit laws, The precise definition of a limit
- Week 03:One-sided limits ,continuity, limits involving infinity: asymptotes of graphs
- Week 04: Differentiation: tangent and derivative at a point, the derivative as a function
- Week 05: Differentiation rules, the derivative as a rate of change
- Week 06: Derivative of trigonometric functions, chain rule, implicit differentiation.
- Week 7: Related rates, linearization and differentials, higher derivatives.
- Week 8: Applications of derivatives: extreme values of functions
- Week 09: Mid Term Exam
- Week 10: Rolle's theorem, the mean value theorem, Monotonic functions and the first derivative test
- Week 11:Applied optimization, Antiderivatives, integration: area and estimating with finite sums
- Week 12: Sigma notation and limits of finite sums, definite integral, the fundamental theorem of calculus
- Week 13: Applications of definite integrals :volume using cross-sections
- Week 14: Volumes using cylindrical shells, arc length, Areas of surfaces of revolution
- Week 15:Transdental functions: inverse functions and their derivatives, Cauchy’s residue theorem with applications
- Week 16: Natural logarithms, exponential functions, indeterminate forms and L' Hospital's rule
- Week 17:Inverse trigonometric functions, hyperbolic functions.
- Week 18: Final Term Exam
- Chapters 18
- Department Mathematics
- Teacher
Ms. Asifa Ilyas
