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• Week 1: Preliminaries: Real numbers, intervals, distance formula, equations and graphs of circle and line
• Week 2: Functions of one variable and their graphs, shifting of graphs
• Week 3: Trigonometric functions, exponential functions, inverse functions and logarithms
• Week 4: Rates of change and tangents to curves, Limit of a function and limit laws, the precise definition of a limit
• Week 5: One-sided limits, continuity, limits involving infinity; asymptotes of graphs
• Week 6: Differentiation: tangents and derivative at a point, the derivative as a function, differentiation rules,
• Week 7: The derivative as a rate of change, derivatives of trigonometric functions, chain rule
• Week 8: Implicit differentiation, related rates, linearization and differentials
• Week 9: Winter break, December 21 - 24, 2020
• Week 10: Mid Term Exams, December 28, 2020 - January 01, 2021
• Week 11: Applications of derivatives: extreme values of functions, Rolls’ theorem, the mean value theorem, monotonic functions and the first derivative test, concavity and curve sketching
• Week 12: Indeterminate forms and L'Hôpital's rule, antiderivatives,
• Week 13: Integration: area and estimating with finite sums, sigma notation and limits of finite sums, the definite integral
• Week 14: The fundamental theorem of calculus , indefinite integrals and the substitution method
• Week 15: Applications of definite integrals: volumes using cross-sections, volumes using cylindrical shells,
• Week 16: arc length, areas of surfaces of revolution
• Week 17: Work and fluid forces, moments and center of mass
• Week 18: Revision
• Week 19: Final Term Examination