Delve into advanced calculus concepts in this comprehensive 12-hour course covering inverse functions, exponential and logarithmic functions, derivatives, integration techniques, differential equations, sequences, and series. Master topics such as l'Hôpital's Rule, integration by parts, trigonometric integrals, partial fractions, Euler's method, linear equations, predator-prey systems, and Taylor and Maclaurin series. Develop problem-solving skills through various applications and gain a deeper understanding of calculus principles essential for further mathematical studies and real-world applications.
Overview
Syllabus
6.1 part 1 - Inverse Functions.
6.1 part 2 - Inverse Functions.
6.2 part 1 - Exponential Functions and Their Derivatives.
6.2 part 2 - Exponential Functions and Their Derivatives.
6.3 - Logarithmic Functions.
6.4 part 1 - Derivatives of Logarithmic Functions.
6.4 part 2 - Derivatives of Logarithmic Functions.
6.4 part 3 - Derivatives of Logarithmic Functions.
6.5 part 1 - Exponential Growth and Decay.
6.5 part 2 - Exponential Growth and Decay.
6.6 part 1 - Inverse Trigonometric Functions.
6.6 part 2 - Inverse Trigonometric Functions.
6.7 part 1 - Hyperbolic Functions.
6.7 part 2 - Hyperbolic Functions.
6.8 part 1 - Indeterminate Forms and l'Hopital's Rule.
6.8 part 2- Indeterminate Forms and l'Hopital's Rule.
6.8 part 3- Indeterminate Forms and l'Hopital's Rule.
7.1 part 1 - Integration by Parts.
7.1 part 2 - Integration by Parts.
7.1 part 3 - Integration by Parts.
7.2 part 1 - Trigonometric Integrals.
7.2 part 2- Trigonometric Integrals.
7.2 part 3 - Trigonometric Integrals.
7.3 part 1 - Trigonometric Integrals.
7.3 part 2 - Trigonometric Substitution.
7.4 - Integration of Rational Functions by Partial Fractions.
7.5 - Strategy for Integration.
7.7 part 1 - Approximate Integration.
7.7 part 2 - Approximate Integration.
7.7 part 3 - Approximate Integration.
8.4 - Applications.
9.2 part 1 - Direction Fields and Euler's Method.
9.2 part 2 - .irection Fields and Euler's Method.
9.5 part 1 - Linear Equations.
9.5 part 2 - Linear Equations.
9.6 - Predator-Prey Systems.
11.1 part 1 - Sequences.
11.1 part 2 - Sequences.
11.1 part 3 - Sequences.
11.2 part 1 - Series.
11.2 part 2 - Series.
11.2 part 3 - Series.
11.3 part 1 - The Integral Test and Estimates of Sums.
11.3 part 2 - The Integral Test and Estimates of Sums.
11.4 part 1 - Comparison Tests.
11.4 part 2 - The Comparison Tests.
11.5 part 1 - Alternating Series.
11.5 part 2 - Alternating Series.
11.6 part 1 - Absolute Convergence and the Ratio and Root Tests.
11.6 part 2 - Absolute Convergence and the Ratio and Root Tests.
11.7 - Strategy for Testing Series.
11.8 part 1 - Power Series.
11.8 part 2 - Power Series.
11.10 part 1 - Taylor and Maclaurin Series.
11.10 part 2 - Taylor and Maclaurin Series.
11.10 part 3 - Taylor and Maclaurin Series.
11.10 part 4 - Taylor and Maclaurin Series.
Taught by
Kamuela Yong
