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**Guide to Essential Math A review for Physics, Chemistry and Engineering Students ** written by
** S. M. Blinder **, University of Michigan, Ann Arbor, USA.

This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) which is needed to succeed in science courses. The focus is on math actually used in physics, chemistry and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. By the author's design, no problems are included in the text, to allow the students to focus on their science course assignments. - Highly accessible presentation of fundamental mathematical techniques needed in science and engineering courses - Use of proven pedagogical techniques develolped during the author's 40 years of teaching experience - illustrations and links to reference material on World-Wide-Web - Coverage of fairly advanced topics, including vector and matrix algebra, partial differential equations, special functions and complex variables.

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**Guide to Essential Math A review for Physics, Chemistry and Engineering Students ** written by
** S. M. Blinder **
cover the following topics.
**1. Mathematical Thinking**

1.1 The NCAA March Madness Problem

1.2 Gauss and the Arithmetic Series

1.3 The Pythagorean Theorem

1.4 Torus Area and Volume

1.5 Einstein’s Velocity Addition Law

1.6 The Birthday Problem

1.7 Fibonacci Numbers and the Golden Ratio

1.8 vp in the Gaussian Integral

1.9 Function Equal to Its Derivative

1.10 Log of N Factorial for Large N

1.11 Potential and Kinetic Energies.

1.12 Riemann Zeta Function and Prime Numbers

1.13 How to Solve It

1.14 A Note on Mathematical Rigor
**2. Numbers**

2.1 Integers.

2.2 Primes.

2.3 Divisibility

2.4 Rational Numbers

2.5 Exponential Notation.

2.6 Powers of 10

2.7 Binary Number System.

2.8 Infinity
**3. Algebra**

3.1 Symbolic Variables

3.2 Legal and Illegal Algebraic Manipulations.

3.3 Factor-Label Method

3.4 Powers and Roots.

3.5 Logarithms.

3.6 The Quadratic Formula

3.7 Imagining

3.8 Factorials, Permutations, and Combinations

3.9 The Binomial Theorem.

3.10 e Is for Euler
**4. Trigonometry**

4.1 What Use Is Trigonometry?.

4.2 The Pythagorean Theorem.

4.3 p in the Sky

4.4 Sine and Cosine

4.5 Tangent and Secant

4.6 Trigonometry in the Complex Plane.

4.7 de Moivre’s Theorem

4.8 Euler’s Theorem

4.9 Hyperbolic Functions
**5. Analytic Geometry**

5.1 Functions and Graphs

5.2 Linear Functions.

5.3 Conic Sections

5.4 Conic Sections in Polar Coordinates.
**6. Calculus
6.1 A Little Road Trip
6.2 A Speedboat Ride.
6.3 Differential and Integral Calculus
6.4 Basic Formulas of Differential Calculus
6.5 More on Derivatives
6.6 Indefinite Integrals
6.7 Techniques of Integration
6.8 Curvature, Maxima, and Minima
6.9 The Gamma Function
6.10 Gaussian and Error Functions
**

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- Vector Analysis
- Tensor Calculus
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- Discrete Mathematics

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- Math Magic
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