Week 7: The derivative as a rate of change, derivatives of trigonometric functions, chain rule
Thomas Calculus, Early Transcendentals, (13th edition)
Sec 3.4 The Derivative as a Rate of Change (pages: 146 - 155)
In this section we study further applications in which derivatives model the rates at which things change. It is natural to think of a quantity changing with respect to time, but other variables can be treated in the same way. For example, an economist may want to study how the cost of producing steel varies with the number of tons produced, or an engineer may want to know how the power output of a generator varies with its temperature.
Sec 3.5 Derivatives of Trigonometric Functions (pages: 156 - 162)
Many phenomena of nature are approximately periodic (electromagnetic fields, heart rhythms, tides, weather). The derivatives of sines and cosines play a key role in describing periodic changes. This section shows how to differentiate the six basic trigonometric functions.
Sec 3.6 The Chain Rule (pages: 163 - 171)
We develop the chain rule in this section.
- 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
- Chapters 19
- Department Chemistry
- Teacher
Dr. Uzma Ahmad
