A Handbook of Mathematical Methods and Problem-Solving Tools for Introductory Physics

✍ Scribed by Joshua F. Whitney

• Publisher: IOP Publishing
• Year: 2021
• Tongue: English
• Leaves: 91
• Series: IOP Expanding Physics
• Edition: 2
• Category: Library

✦ Synopsis

This is a companion textbook for an introductory course in physics. The purpose is to thoroughly link the theories students learn in class with actual problem-solving techniques. In other words, it addresses the common complaint that 'I feel like I understand the concepts, but I can't do the homework'. This book covers the fundamentals that comprise the majority of a physics course in as simple and concise terms as possible, with a particular emphasis on how the fundamental concepts and equations allow students to solve problems. In addition to updates across the board, this edition includes new material relating to waves, optics, fields, magnetism, and circuits. Each section focuses on a deeper understanding of the equations you will be using along with problem-solving skills. Remember that equations themselves are merely tools and you will be in much better shape if you know what tool you are looking for before you start looking. The book will equip you with the problem-solving techniques and conceptual explanations that can be applied to almost anything in your introductory physics course.

Key Features

• Extensively updated and extended
• Student-friendly
• Targeted and concise descriptions of each theme
• Worked examples
• Introduces problem-solving techniques and conceptual explanations that can be applied to almost anything in an introductory physics course

✦ Table of Contents

PRELIMS.pdf
About the authors
Joshua F Whitney and Heather M Whitney
CH001.pdf
Chapter 1 Introduction
CH002.pdf
Chapter 2 Kinematics
2.1 Equations needed with symbols defined
2.2 Understanding the equations
2.3 Keeping the signs straight
2.4 Motion in two dimensions: relating x and y
2.5 Summary and important notes
CH003.pdf
Chapter 3 Newton’s laws
3.1 Applying the first law
3.2 Applying the second law
3.3 Applying the third law
3.4 Examples
Applying the first and second laws
Applying the third law
Applying all three laws together
3.5 Summary and important notes
CH004.pdf
Chapter 4 Energy and momentum
4.1 Energy
4.2 Example
4.3 Momentum
4.4 Types of collisions
4.5 Summary and important notes
CH005.pdf
Chapter 5 Circular and rotational motion
5.1 Centripetal force
5.2 Torque
5.2.1 Moment of inertia
5.3 Waves
5.4 Oscillations
5.4.1 Wavelength and period (λ, T, or τ)
5.4.2 Frequency (f or ν)
5.4.3 Angular frequency (ω)
5.4.4 Wave number (k)
5.4.5 Phase angle (ϕ)
5.4.6 Quick reference guide for descriptions of oscillations
5.5 Traveling waves
5.6 Standing waves and boundary conditions
CH006.pdf
Chapter 6 Basic optics
6.1 Diffraction and interference
6.2 Thin lenses
6.3 Summary and important notes
CH007.pdf
Chapter 7 The right-hand rule
7.1 How to use it properly
7.2 Special case of magnetic fields from currents
7.3 Summary and important notes
CH008.pdf
Chapter 8 Electric fields and electric potential
8.1 Finding fields and forces from point charges
8.1.1 Electric field integrals
8.2 Electric potential from point charges
8.3 Summary and important notes
CH009.pdf
Chapter 9 Magnetic fields
9.1 Biot–Savart law
9.1.1 Right-hand rule for magnetic fields
9.1.2 Calculations with the Biot–Savart law
Example 1
Example 2
9.2 Magnetic forces
Example 3
9.3 Trigonometry for electric and magnetic field integrals
Example 4
9.4 Induced currents: Faraday’s and Lenz’s law
Example 5
CH010.pdf
Chapter 10 Circuits
10.1 Ohm’s law
10.2 Kirchhoff’s loop and junction laws
10.2.1 Loop law: the sum of the potential differences around a closed circuit is zero
Example 6
10.2.2 Junction law: the sum of all currents into a junction must be equal to the sum of the currents out of the junction
Example 7
10.3 Summary and important notes
CH011.pdf
Chapter 11 Modern physics
11.1 Relativity
11.1.1 Time dilation
11.1.2 Length contraction
11.1.3 Lorentz velocity transformations
11.2 Quantum mechanics
11.2.1 The photoelectric effect
11.2.2 Electron transitions
11.2.3 Wavefunctions and probability
11.3 Brief aside on energy equations
11.4 Summary and important notes
CH012.pdf
Chapter 12 General problem-solving tips
12.1 Break the problem down into as small pieces as possible
12.2 Write down everything you have and what you are trying to find
12.3 Check units
12.4 Pull all the 10n factors out of your calculation before putting it in your calculator
12.5 Practice algebra
12.6 Keep everything symbolic as long as possible
12.7 Electron volts