Introduction -- Math fundamentals: Solving equations ; Numbers ; Variables ; Functions and their inverses ; Fractions ; Basic rules of algebra ; Solving quadratic equations ; Exponents ; Logarithms ; The number line ; Inequalities ; The Cartesian plane ; Functions ; Function reference ; Polynomials ; Trigonometry ; Trigonometric identities ; Geometry ; Circle ; Ellipse ; Hyperbola ; Solving systems of linear equations ; Compound interest ; Set notation ; Math problems -- Introduction to physics: Introduction ; Kinematics ; Introduction to calculus ; Kinematics with calculus ; Kinematics problems -- Vectors: Great outdoors ; Vectors ; Basis ; Vector products ; Complex numbers ; Vectors problems -- Mechanics: Introduction ; Projectile motion ; Forces ; Force diagrams ; Momentum ; Energy ; Uniform circular motion ; Angular motion ; Simple harmonic motion ; Conclusion ; Mechanics problems -- Calculus: Introduction ; Overview ; Infinity ; Limits ; Limit formulas ; Derivatives ; Derivative formulas ; Derivative rules ; Higher derivatives ; Optimization algorithm ; Implicit differentiation ; Integrals ; Riemann sums ; The fundamental theorem of calculus ; Techniques of integration ; Applications of integration ; Improper integrals ; Sequences ; Series ; Conclusion ; Calculus problems -- End matter : Conclusion -- A. Answers and solutions -- B. Notation: Math notation ; Set notation ; Complex numbers notation ; Vectors notation ; Mechanics notation ; Calculus notation -- C. Constants, units and conversion ratios: Fundamental constants of nature ; Units ; Derived units ; Other units and conversions -- D. SymPy tutorial -- E. Formulas : Calculus formulas ; Mechanics formulas.
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"This book contains lessons on topics in math and physics, written in a style that is jargon-free and to the point. Each lesson covers one concept at the depth required for the first-year university-level course. The main focus of this book is to highlight the intricate connections between the concepts of math and physics. Seeing the similarities and parallels between the concepts is the key to understanding."--Preface.