This course on Calculus II aims to teach students the following learning outcomes and goals:
- Understanding general and particular solutions to differential equations
- Solving differential equations using separation of variables
- Applying integration techniques to find areas, volumes, arc lengths, and surface areas
- Exploring sequences, series, and power series
- Studying conic sections, parametric equations, and polar coordinates
The course covers individual skills such as:
- Solving differential equations
- Integrating functions using various methods
- Analyzing sequences and series
- Graphing conic sections and polar equations
The teaching method of the course involves video lectures corresponding to chapters 6-10 of a specific calculus textbook.
The intended audience for this course includes students studying advanced calculus topics, particularly those interested in mathematics, engineering, or physical sciences.
Overview
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.
Taught by
Kimberly Brehm
