Overview

Dive into an extensive 18-hour course covering Calculus II, corresponding to chapters 6-10 of Calculus 11e by Larson and Edwards. Master differential equations, integration techniques, sequences and series, and conic sections. Explore topics such as slope fields, exponential growth models, volume calculations using various methods, improper integrals, convergence tests for infinite series, power series, and parametric equations. Gain practical skills in solving complex mathematical problems and applying calculus concepts to real-world scenarios. Enhance your understanding of advanced calculus topics through comprehensive lectures and examples, preparing you for further studies in mathematics and related fields.

Syllabus

Calculus II - 6.1.1 General and Particular Solutions to Differential Equations.
Calculus II - 6.1.2 Slope Fields.
Calculus II - 6.2.1 Use Separation of Variables to Solve a Simple Differential Equation.
Calculus II - 6.2.2 Models of Exponential Growth and Decay.
Calculus II - 6.3.1 Using Separation of Variables to Find General and Particular Solutions.
Calculus II - 6.3.2 The Logistic Differential Equation.
Calculus II - 6.4.1 First Order Linear Differential Equations.
Calculus II - 7.1.1 Finding The Area Under a Curve.
Calculus II - 7.1.2 Finding the Area Between Two Curves.
Calculus II - 7.1.3 Applications Involving the Area Between Two Curves.
Calculus II - 7.2.1 Finding Volume Using the Disk Method.
Calculus II - 7.2.2 Finding Volume Using the Washer Method.
Calculus II - 7.2.3 Finding the Volume of a Solid with Known Cross Sections.
Calculus II - 7.3.1 Finding Volume Using the Shell Method.
Calculus II - 7.3.2 Disk Method vs. Shell Method.
Calculus II - 7.4.1 Finding Arc Length.
Calculus II - 7.4.2 Surfaces of Revolution.
Calculus II - 7.5.1 Work, Work, Work.
Calculus II - 7.6.1 Center of Mass in a One- or Two-Dimensional System.
Calculus II - 7.6.2 Center of Mass of a Planar Lamina.
Calculus II - 7.7.1 Fluid Pressure and Fluid Force.
Calculus II - 8.1.1 Fitting Integrands to Basic Integration Rules.
Calculus II - 8.2.1 Integration by Parts.
Calculus II - 8.3.1 Integrals Involving Powers of Sine and Cosine.
Calculus II - 8.3.2 Integrals Involving Powers of Secant and Tangent.
Calculus II - 8.4.1 Trigonometric Substitution.
Calculus II - 8.5.1 Using Partial Fractions with Linear Factors to Integrate.
Calculus II - 8.5.2 Using Partial Fractions with Quadratic Factors to Integrate.
Calculus II - 8.6.1 Using the Trapezoidal Rule to Approximate Integrals.
Calculus II - 8.6.2 Using Simpson's Rule to Approximate Integrals.
Calculus II - 8.8.1 Improper Integrals with Infinite Limits of Integration.
Calculus II - 8.8.2 Improper Integrals with Infinite Discontinuities.
Calculus II - 9.1.1 The Limit of a Sequence.
Calculus II - 9.1.2 Pattern Recognition for Sequences.
Calculus II - 9.1.3 Monotonic and Bounded Sequences.
Calculus II - 9.2.1 Infinite Series.
Calculus II - 9.2.2 The Geometric Series.
Calculus II - 9.2.3 The nth Term Test for Divergence.
Calculus II - 9.3.1 The Integral Test.
Calculus II - 9.3.2 The p-Series.
Calculus II - 9.4.1 The Direct Comparison Test.
Calculus II - 9.4.2 The Limit Comparison Test.
Calculus II - 9.5.1 The Alternating Series Test.
Calculus II - 9.5.2 The Alternating Series Remainder.
Calculus II - 9.5.3 Absolute and Conditional Convergence.
Calculus II - 9.6.1 The Ratio Test.
Calculus II - 9.6.2 The Root Test.
Calculus II - 9.8.1 The Power Series L=0 or L=Inf.
Calculus II - 9.8.2 The Power Series - Finding R and the Interval of Convergence.
Calculus II - 9.9.1 Represent Functions with the Geometric Power Series.
Calculus II - 9.9.2 Operations with The Geometric Power Series.
Calculus II - 9.10.1 The Taylor and Maclaurin Series.
Calculus II - 9.10.2 The Binomial Series.
Calculus II - 9.10.3 Use The Power Series for Elementary Functions.
Calculus II - 10.1.1 An Introduction to Conic Sections.
Calculus II - 10.1.2 Parabolas.
Calculus II - 10.1.3 Ellipses.
Calculus II - 10.1.4 Hyperbolas.
Calculus II - 10.2.1 Plane Curves and Parametric Equations.
Calculus II - 10.2.2 Finding Parametric Equations.
Calculus II - 10.3.1 Slope, Tangent Lines, and Concavity of Parametric Equations.
Calculus II - 10.4.1 Polar Coordinates and Coordinate Conversion.
Calculus II - 10.4.2 Polar Graphs.
Calculus II - 10.4.3 Slope and Tangent Lines of Polar Equations.