In this page I link to my math curriculum. After finishing intermediate algebra, I'm focusing on calculus.
Here are the books that I completed including all exercises:
The calculus problems I'm posting here are quite interesting. Textual questions are usually most challenging. I'm learning from several sources. Currently, I'm learning from the Servay, Jewett Physics text book.
I have a few separate pages that display video tutorials and text tutorials and my intermediate/advanced math exercises in the following topics
- Parametric vector fields and the Green's Theorem: Introduction
- Calculus: Infinite series: http://motifsbyvincent.blogspot.com/p/calculus-infinite-series.html
- Putnam Exam Challenges: http://motifsbyvincent.blogspot.com/p/putnam-challenges.html
- Integration techniques: http://motifsbyvincent.blogspot.com/p/calculus.html
- Calculus: Shell, Ring Volume Calculations, Indefinite Integrals: http://motifsbyvincent.blogspot.com/p/robotic-systems.html
- Pre-calculus topics http://motifsbyvincent.blogspot.com/p/pre-calculus-topics.html
- Calculus: Alternating Series: http://motifsbyvincent.blogspot.com/p/calculus-alternating-series.html
- The rod density problem
Calculus and Kinematics
- One dimensional kinematics: two falling bodies
- One dimensional kinematics: deriving kinematics formulas through calculus
- Integrating vectors representing motion: evaluating a vector function through integration
- Key aspect of movement in two dimensions under acceleration
P.2 Linear Models and Rates of Change
P.3 Functions and Their Graphs
Limits and their properties
1.2 Finding Limits Graphically and Numerically
1.3 Evaluating Limits Analytically
1.5 Infinite Limits
Differentiation
2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.5 Implicit Differentiation
Applications of Differentiation
3.3 Increasing and Decreasing Functions and the First Derivative Test
3.5 Limits at Infinity
3.9 Differentials
Integration
4.1 Antiderivatives and Indefinite Integration
4.2 Area
4.5 Integration by Substitution
Logarithmic, Exponential and Other Transcendental Functions
5.2 The Natural Logarithmic Function: Integration
5.3 Inverse Functions
5.7 Inverse Trigonometric Functions: Integration
Differential Equations
6.1 Slope Fields and Euler’s Method
6.3 Separation of Variables and the Logistic Equation
6.4 First-Order Linear Differential Equations
Applications of Integration
7.1 Area of a Region Between Two Curves
7.2 Volume: The Disk Method
7.3 Volume: The Shell Method
Integration Techniques, L’Hopital’s Rule and Improper Integrals
8.1 Basic Integration Rules
8.2 Integration by Parts
8.3 Trigonometric Substitution
Infinite Series (To Be Done)
Conics, Parametric Equations and Polar Coordinates
10.1 Conics and Calculus
10.4 Polar Coordinates and Polar Graphs
10.5 Area and Arc Length in Polar Coordinates
Vectors and the Geometry of Space (Current)
