Alignment: Calculus • Michael Spivak • Fourth Edition

Use Nagwa in conjunction with your preferred textbook. The recommended lessons from Nagwa for each section of this textbook are provided below. This alignment is not affiliated with, sponsored by, or endorsed by the publisher of the referenced textbook. Nagwa is a registered trademark of Nagwa Limited. All other trademarks and registered trademarks are the property of their respective owners.

• Part I Prologue
• 1 Basic Properties of Numbers
• 2 Numbers of Various Sorts
• Part II Foundations
• 3 Functions
• Appendix: Ordered Pairs
• 4 Graphs
• Appendix 1: Vectors
• Appendix 2: The Conic Sections
• Appendix 3: Polar Coordinates
• 5 Limits
• 6 Continuous Functions
• 7 Three Hard Theorems
• 8 Least Upper Bounds
• Appendix: Uniform Continuity
• Part III Derivatives and Integrals
• 9 Derivatives
• 10 Differentiation
• 11 Significance of the Derivative
• Appendix: Convexity and Concavity
• 12 Inverse Functions
• Appendix: Parametric Representation of Curves
• 13 Integrals
• Appendix: Riemann Sums
• 14 The Fundamental Theorem of Calculus
• 15 The Trigonometric Functions
• 16 𝜋 is Irrational
• 17 Planetary Motion
• 18 The Logarithm and Exponential Functions
• 19 Integration in Elementary Terms
• Appendix: The Cosmopolitan Integral
• Part IV Infinite Sequences and Infinite Series
• 20 Approximation by Polynomial Functions
• 21 𝘦 is Transcendental
• 22 Infinite Sequences
• 23 Infinite Series
• 24 Uniform Convergence and Power Series
• 25 Complex Numbers
• 26 Complex Functions
• 27 Complex Power Series
• Part V Epilogue
• 28 Fields
• 29 Construction of the Real Numbers
• 30 Uniqueness of the Real Numbers