Handbook of Mathematical Methods and Problem-Solving Tools for Introductory Physics, 2nd Edition
- Length: 120 pages
- Edition: 2
- Language: English
- Publisher: Iop Publishing Ltd
- Publication Date: 2021-08-31
- ISBN-10: 0750333979
- ISBN-13: 9780750333979
- Sales Rank: #9250252 (See Top 100 Books)
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
Cover Title Copyright Contents About the authors 1 Introduction 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 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 3.5 Summary and important notes 4 Energy and momentum 4.1 Energy 4.2 Example 4.3 Momentum 4.4 Types of collisions 4.5 Summary and important notes 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 6 Basic optics 6.1 Diffraction and interference 6.2 Thin lenses 6.3 Summary and important notes 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 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 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 9.2 Magnetic forces 9.3 Trigonometry for electric and magnetic field integrals 9.4 Induced currents: Faraday’s and Lenz’s law 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 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 10.3 Summary and important notes 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 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
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