Prologue : what is a function? -- 1. Let's differentiate a function -- Approximating with functions -- Calculating the relative error -- The derivative in action -- Calculating the derivative -- Calculating the derivative of a constant, linear, or quadratic function -- 2. Let's learn differentiation techniques -- The sum rule of differentiation -- The product rule of differentiation -- Differentiating polynomials -- Finding maxima and minima -- Using the mean value theorem -- Using the quotient rule of differentiation -- Calculating derivatives of composite functions -- Calculating derivatives of inverse functions -- 3. Let's integrate a function -- Illustrating the fundamental theorem of calculus -- When the density is constant -- When the density changes stepwise -- When the density changes continuously -- Review of the imitating linear function -- Approximation vs. exact value -- Using the fundamental theorem of calculus -- Using integral formulas -- Applying the fundamental theorem -- Supply curve -- Demand curve -- Review of the fundamental theorem of calculus -- Formula of the substitution rule of integration -- The power rule of integration -- 4. Let's learn integration techniques -- Using trigonometric functions -- Using integrals with trigonometric functions -- Using exponential and logarithmic functions -- Integration by parts -- 5. Let's learn about Taylor Expansions -- Imitating with polynomials -- How to obtain a Taylor expansion -- Taylor expansion of various functions -- 6. Let's learn about partial differentiation -- What are multivariable functions? -- Basics of variable linear functions -- Partial differentiation -- Total differentials -- Conditions for extrema -- Applying partial differentiation to economics -- The chain rule -- Derivatives of implicit functions -- Epilogue: what is mathematics for? -- A. Solutions to exercises -- B. Main formulas, theorems, and functions covered in this book -- Linear equations (Linear functions) -- Differentiation -- Derivatives of popular functions -- Integrals -- Taylor expansion -- Partial derivatives.