21C (Calculus)

Notes by Topic  *Videos for some of these notes are here

Sequences 

The nth Term (Divergence) Test and Sequence of Partial Sums Test 

Geometric Series, P-Series, and Integral Tests Bouncing Ball Paradox Von Koch Snowflake 

Direct Comparison, Limit Comparison, and Ratio Tests 

The Root and Alternating Series Tests 

Tricky Examples (Root and Ratio Tests) 

Power Series and Finding the Interval/Radius of Convergence 

A Tricky Radius of Convergence Problem

Manipulating a Power Series to Find the Sum of an Infinite Series 

Taylor's Formula  

Sum of p-series (p = 2)  

Two Ways to Find Maclaurin Series for ln(5 + x)  

First 4 Terms of Maclaurin Series for f(x)=sin(3arctan(6x)) 

Power Series for f(x) = ln(9+x)/(8-x) Using Series Multiplication 

Using a Taylor Polynomial to Approximate an Integral 

Using a Power Series to Estimate an Integral 

The Binomial Series and Taylor's Remainder Theorem 

Euler's Formula and Trig Identites 

Using Euler's Formula to Find the Sum of a Series

Introduction to 3D Graphing 

Intro to Vectors, Dot Product, Projections 

The Cross Product with Applications 

How to Find the Volume of a Parallelpiped when Given All 8 Vertices 

Lines in Parametric Form 

How to Tell if Two Lines Intersect, are Parallel, or Skew 

Distance From a Point to a Line 

Distance From a Point to a Plane 

Distance Between Skew Lines 

Finding the Angle Between Two Planes and the Equation of the Line of Intersection 

Vector Valued Functions 

Vector-Valued Functions and Motion in Space (Circles) 

The Cycloid (A cool curve!) 

Find a Position Vector from an Acceleration Vector 

Projectile Motion Example 

 Unit Tangent and Normal Vectors, Curvature   *Not always covered in 21C!

Domain, Range and Level Curves 

Why the Empty Set is Both Open and Closed 

Evaluating Limits for Functions of Two Variables 

Partial Derivatives 

Using the Limit Definition of a Partial Derivative 

Showing a Function is Differentiable at a Point 

Differentiable But Not Continuous 

The Chain Rule for Derivatives of Multivariable Functions 

Chain Rule (2nd Derivative) 

Chain Rule (Derivative of an Integral) 

Directional Derivatives and the Gradient Vector 

Direction for a Specific Directional Derivative 

Temperature of a Particle Moving Through Space 

Tangent Planes and Linearizations 

Finding Extrema for Functions of Two Variables 

The Lagrange Multiplier Method 

Tricky Lagrange Problem 

Partial Derivatives With Constrained Variables   *Not always covered in 21C!

Problem Sets and Solutions

PS1 (Sequences, nth Term Test) PS1 Solutions 

PS2 (Geometric, Integral and p-Series Tests) PS2 Solutions 

PS3 (Comparison and Ratio Tests) PS3 Solutions 

PS4 (Root and Alternating Series Tests) PS4 Solutions 

PS5 (Power Series and Interval of Convergence) PS5 Solutions 

PS6 (Taylor's Formula) PS6 Solutions 

PS7 (Binomial Series and Applied Power Series) PS7 Solutions  

PS7B (Intro to 3D Graphing)

PS8 (Intro to Vectors, Dot Product) PS8 Solutions 

PS9 (Cross Product and Applications) PS9 Solutions 

PS10 (Vector Applications) PS10 Solutions 

PS11 (Vector Functions, Projectile Motion) PS11 Solutions 

PS12 (Unit Tangent and Normal Vectors) 

PS13 (Domain, Range, Limits for 2 Variable Functions) PS13 Solutions 

PS14 (Partial Derivatives) PS14 Solutions 

PS15 (Directional Derivatives and the Gradient) PS15 Solutions 

PS16 (Tangent Planes and Linearizations) PS16 Solutions 

PS17 (Finding Local and Absolute Extrema) PS17 Solutions 

PS18 (Lagrange Multiplier Method) PS18 Solutions 

Exam Review Problems

Midterm 1 Review   Midterm 1 Review (Solutions) 

Midterm 2 Review Midterm 2 Review (Solutions) 

Midterm 3 Review Midterm 3 Review (Solutions)

Final Review Final Review (Solutions)