Week 3: Trigonometric functions, exponential functions, inverse functions and logarithms
Thomas Calculus, Early Transcendentals (13th edition)
Sec 1.3 Trigonometric Functions (pages: 21 - 28)
This section reviews radian measure and the basic trigonometric functions.
Sec 1.5 Exponential Functions (pages: 36 - 41)
Exponential functions are among the most important in mathematics and occur in a wide variety of applications, including interest rates, radioactive decay, population growth, the spread of a disease, consumption of natural resources, the earth’s atmospheric pressure, temperature change of a heated object placed in a cooler environment, and the dating of fossils. In this section we introduce these functions informally, using an intuitive approach.
Sec 1.6 Inverse Functions and Logarithms (pages: 41 - 54)
A function that undoes, or inverts, the effect of a function ƒ is called the inverse of ƒ. Many common functions, though not all, are paired with an inverse. In this section we present the natural logarithmic function y = ln x as the inverse of the exponential function y = exp(x), and we also give examples of several inverse trigonometric functions.
- 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
