You will want to study basic mathematics before you get into mechanics.

For what follows these are good resources:

**US Navy Training Manual, Mathematics, Basic Math and Algebra**, search for NAVEDTRA 14139 in your search engine.**US Navy Training Manual. Mathematics, Trigonometry**, search for NAVEDTRA 14140 in your search engine.**US Navy Training Manual. Mathematics, Pre-Calculus and Introduction to Probability**, search for NAVEDTRA 14141 in your search engine.**US Navy Training Manual. Mathematics, Introduction to Statistics, Number Systems and Boolean Algebra**, search for NAVEDTRA 14142 in your search engine.- David A. Santos, (2008),
**Andragogic Propaedeutic Mathematics**. This is a free download for the website: http://www.opensourcemath.org/books/santos/santos-a-course-in-arithmetic.pdf. This book does not cover complex numbers, but it does have an introduction to sets. - David A. Santos, (2008),
**Ossifrage and Algebra**. This is a free download for the website: http://www.opensourcemath.org/books/santos/santos-elementary_algebra_book.pdf. This book does not cover complex numbers. - David A. Santos, (2008),
**Precalculus**. This is a free download for the website: http://www.opensourcemath.org/books/santos/santos-precalculus.pdf. - Silvanus Thompson, (1912),
**The Project Gutenberg EBook of Calculus Made Easy**. Note that this has been redone with modern notation throughout. This is a free download from the website: http://www.gutenberg.org/files/33283/33283-pdf.pdf - David Santos, (2008),
**The Elements of Infinitesimal Calculus**. This is a free download for the website: http://www.opensourcemath.org/books/santos/santos-very-basic-calculus.pdf - S. K. Chung, (2007),
**Understanding Basic Calculus**. This is a free download from the website: http://www.mathdb.org/basic_calculus/BasicCalculus.pdf - David Guichard, (2012),
**Calculus Early Transcendentals**. This is a free download from the website: http://www.whitman.edu/mathematics/multivariable/ - Wilfrid Kaplan and Donal J. Lewis, (),
**Calculus and Linear Algebra, vol.s 1 and 2**. These are a free downloads from the website: http://quod.lib.umich.edu/s/spobooks/. I strongly recommend these. - Dan Sloughter, (2000),
**Difference Equations to Differential Equations**, as a free download located here: http://synechism.org/drupal/de2de/. - Kenneth Kuttle, (2010),
**Calculus, Applications and Theory**. A free download from the website: http://www.math.byu.edu/~klkuttle/calcbookBshortold.pdf - Feynman, Lieghton, Sands,
**The Feynman Lectures on Physics**, Now available for online reading at: http://www.feynmanlectures.caltech.edu/index.html.

If you wish to buy a book, I recommend these:

- Biman Das, (2005),
**Mathematics for Physics with Calculus**, Pearson Prentice Hall. The only problem with this book is that it doesn't cover any linear algebra. - George E. Owen, (1964),
**Fundamentals of Scientific Mathematics**, Johns Hopkins University Press, reprinted by Dover Publications in 2003. This is a very nice book to read, covering the use of matices in geometry, vector algebra, analytic geometry, functions and approximations, and calculus. - Feynman, Leighton, Sands,
**The Feynman Lecture on Physics**, Basic Books. I also recommand Feynman, Gottlied, Lighton,**Feynman's Tips on Physics**, Pearson Addison Wesley. And Feynman,**Exercises for the Feynman Lectures on Physics**, Basic Books. - R. Shankar, (2013),
**Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics**. Yale University Press This is well written. - Frank Blume, Calvin Piston, (2014),
**Applied Calculus for Scientists and Engineers, Volume 1**. Available at Amazon.com.

You should master these topics/skills before you move on to mechanics:

This requires either Mathematica 8 or later, or the free Mathematica CDF Viewer, though the viewer cannot run the programs, (you can find that here). You will also need to download the MAST Writing Style into the folder SystemFiles/Front End/Stylesheets. You can download that here. Once you load this file into the folder rename it MAST Writing Style 3. Reload Mathematica and it will be there.

The topics below form several logical units.

This constitutes a modern introductory course in algebra. The key reason to study this, if you altready have studied elementary algebra, is that the language of modern algebraic structures are introdude early and used throughout.

- Numbers and Sets
- Logic:
- Relations
- Binary Operations, Addition, Summation, Multiplication, Products, and Exponentiation
- Semigroups and Solving Equations by Subtraction
- Integers
- Monoids and Groups
- Rings and Integral Domains
- Solving Equations by Division
- Primes, Factoring, and Division
- The Fundametnal Theorem of Arithmetic
- Rational Numbers
- Fields
- Decimal Expansions
- Scientific Notation
- Other Simple Algebraic Structures
- Modular Arithmetic
- Finite Arithmetic
- Diophantine Equations
- Rules for Exponents
- Roots and Logarithms
- Real Numbers
- Dedekind Cuts and Ordered Fields
- Imaginary Numbers
- Complex Numbers
- Quaternions and Gaussian Integers
- Scientific and Mathematical Writing
- Algebraic Expressions
- Polynomials
- Partial Fractions
- The Binomial Theorem
- Combinatorics
- Probability
- Measurement and Error
- Equations
- Functions, Maps, and Morphisms
- Infinite Sets
- Algebraic Functions
- The Theory of Equations
- Exponential and Logarithmic Functions

This is a modern course in introductory geometry where the concepts of geometric symmetry using the language of algebraic structures is used extensively. This merges the concepts of traditional geometry, algebraic structures, trigonometry, analytic geometry, and linear algebra.

- Geometry
- Segments, Rays, and Lines
- Distance and Time
- Angles and Triangles
- Polygons
- Circles and Arcs
- Perimeter and Area
- Constructions
- Congruence and Similarity
- Ratio and Proportion
- Scaling
- Lines and Planes in Space
- Polyhedra
- Round Figures in Space
- Surface Area and Volume
- Estimation
- The Real Line
- Coordinate Systems
- Plotting Data
- Operations on Points
- Plotting Functions
- Transformations
- Right Angle Trigonometry
- General Trigonometry
- Trigonomettric Functions and Periodicity
- Trigonometric Identities
- Matrices, Transformations, and Isometries
- Complex Geometry and de Moivre's Theorem
- Simple Groups
- Linear Systems of Equations
- Determinants
- Dimensional Analysis
- Lines in Coordinate Systems
- Vector Algebra and Geometry
- Inner and Vector Products
- Conic Sections
- Parametric Representation of Curves
- Quadric Surfaces
- Vector Spaces and Linear Mappings
- Quadratic Forms

This consistutes a course in differential and integral calculus.

- Sequences
- Dynamical Systems
- Limits of Sequences
- Limits of Functions
- The Formal Definition of Limits
- Infinity and Limits
- Continuous Functions
- Uniform Continuity
- The Derivative
- Differentiation Rules
- Implicit Differentiation
- Critical Points
- Optimization
- Curve Sketching
- Important Theorems of Differentiation
- Approximations and Differentials
- Related Rates
- Motion in One Dimension
- Riemann Sums
- The Definite Integral
- The Indefinite Integral
- The Fundamental Theorem of Calculus
- Hyperbolic Functions
- Arc Length
- Mean Values
- Areas
- Volumes
- Integrals in Polar Coordinates
- Curvature
- An Introduction to Differential Equations
- The Properties of Integrals
- Integration by Substitution
- Integration by Partial Fractions
- Integration by Parts
- Trigonometric Integrands and Substitutions
- Approximate Integration
- Improper Integrals
- Other Methods of Integration
- Separable and Homogeneous Differential Equations
- First-Order Linear Differential Equations

This extends the ideas of basic calculus.

- Models
- Electric Circuits
- Second-Order Differential Equations
- Electric Circuits II
- Difference Equations
- The Laplace Transform
- Solving Differential Equations by Laplace Transforms
- Continuous Dynamical Systems
- Newton's Equation in One Dimension
- Falling Bodies
- Parachuting
- Probability Distributions
- Random Experiments
- Taylor Polynomials
- Taylor's Theorem
- Infinite Series
- Transformaing Series
- The Preliminary Test
- The Comparison Test
- The Root Test
- The Ratio Test
- The Ratio Comparison Test
- The Integral Test
- Gauss' Test
- Alternating Series
- Absolute and Conditional Convergence
- Operations on Series
- Kummer's Method for Improving Convergence
- Uniform Convergence
- The Weierstrass M Test and Abel's Test
- Properties of Uniformly Convergent Series
- Taylor's Expansion
- Power Series
- Convergence of Power Series
- Operations with Power Series
- Indeterminate Forms
- Inversion of a Power Series
- Tricks for Series Expansions
- Important Series
- Power Series Solution of Differential Equations

Click here to go back to our amateur theoretical physics page.

Click here to go back to our home page.