Single Variable Calculus II Complete Semester Course
See other videos here: https://maultsby.wordpress.ncsu.edu/course-videos/
This is the entire semester of my Calculus II course (MA 241 at NC State University). These videos are based off of my own notes. Here are the four units in this course:
- Techniques of Integration
- Applications of Integration
- Sequences and Series
- Ordinary Differential Equations
Techniques of Integration
- Integration by substitution (u-sub)
- Integration by parts
- Trigonometric integrals 1 (sines and cosines)
- Trigonometric integrals 2 (secants and tangents)
- Trigonometric integrals 3 (tan^2(x) and sec(x))
- Trigonometric integrals 4 (sec^3(x))
- Trigonometric substitution 1
- Trigonometric substitution 2
- Partial Fractions 1
- Partial Fractions 2
- Improper Integrals 1
- Improper Integrals 2
- Improper Integrals 3
- The Trapezoid Rule
- Simpson's Rule
Applications of Integration
- Arclength (34:00)
- Average Value (36:45)
- Force and Work (lifting problems)
- Work done moving a spring (12:44)
- Work pumping fluid from a tank (56:55)
- Force due to hydrostatic pressure (32:22)
- Center of Mass (24:31)
Sequences and Series
Sequences
- Introduction to Sequences (26:08)
- Convergent Sequences (25:23)
- Theorems about the limits of sequences (24:26)
- Optional Supplement: the Monotone Convergence Theorem (19:16)
Series of Numbers
- Introduction to Infinite Series (21:53)
- Test for Divergence (20:06)
- Geometric Series (21:29)
- The Integral Test and p-series (38:24)
- The (Ordinary) Comparison Test (OCT) (29:53)
- The Limit Comparison Test (LCT) (31:53)
- The Alternating Series Test (AST) (47:18)
- Absolute Convergence and the Ratio Test (47:06)
Power Series
- Introduction to Power Series (17:59)
- Interval of Convergence (38:51)
- Finding the radius of convergence (32:50)
- Representing functions as power series (23:24)
- Differentiating Power Series (20:58)
- Integrating Power Series (30:02)
- Power series representation for arctan(x) (14:23) -- This is ultimately the Taylor Series (see below)
- Taylor series coefficients (44:10)
- Famous examples of Taylor series (46:42 total)
Differential Equations (a first look)
First-order ordinary differential equations
- Introduction to Differential Equations (43:16)
- Exponential Growth (16:51)
- Slope Fields (34:11)
- Euler's Method (26:33)
- Separable Differential Equations (35:30)
- Orthogonal Trajectories with Separable Differential Equations (13:35)
- Newton's Law of Cooling (26:05)
- Tank Mixing (50:25)
- The Logistic Model for Growth (30:53)
Second-order ordinary differential equations
- Introduction to Second-Order Linear Differential Equations (22:14)
- Real and distinct roots (11:17)
- One real, repeated root (13:58)
- and complex numbers (15:01)
- Euler's Formula for the complex exponential (18:46)
- Pure imaginary roots (23:11)
- Complex roots (15:41)
- Method of Undetermined Coefficients 1, with example of exponential forcing (21:51)
- Method of Undetermined Coefficients 2, examples with polynomial forcing (22:29)
- Method of Undetermined Coefficients 3, examples with trigonometric forcing (18:10)
- Method of Undetermined Coefficients 4, extra examples (21:15)
- Second-order Differential Equation for Springs (36:24)