CLP-1 Differential Calculus

This textbook covers single variable Differential Calculus.

Calculus Mathematics

Tác giả: Joel Feldman, Andrew Rechnitzer & Elyse Yeager
Nhà xuất bản: University of British Columbia
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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01: The basics
1.01: Numbers
1.02: Sets
1.03: Other Important Sets
1.04: Functions
1.05: Parsing Formulas
1.06: Inverse Functions
02: Limits
2.01: Drawing Tangents and a First Limit
2.02: Another Limit and Computing Velocity
2.03: The Limit of a Function
2.04: Calculating Limits with Limit Laws
2.05: Limits at Infinity
2.06: Continuity
2.07: (Optional) Making the Informal a Little More Formal
2.08: (Optional) Making Infinite Limits a Little More Formal
2.09: (Optional) Proving the Arithmetic of Limits
03: Derivatives
3.01: Revisiting Tangent Lines
3.02: Definition of the Derivative
3.03: Interpretations of the Derivative
3.04: Arithmetic of Derivatives - a Differentiation Toolbox
3.05: Proofs of the Arithmetic of Derivatives
3.06: Using the Arithmetic of Derivatives Examples
3.07: Derivatives of Exponential Functions
3.08: Derivatives of Trigonometric Functions
3.09: One More Tool the Chain Rule
3.10: The Natural Logarithm
3.11: Implicit Differentiation
3.12: Inverse Trigonometric Functions
3.13: The Mean Value Theorem
3.14: Higher Order Derivatives
3.15: (Optional)
04: Applications of derivatives
4.01: Velocity and Acceleration
4.02: Related Rates
4.03: Exponential Growth and Decay a First Look at Differential Equations
4.04: Approximating Functions Near a Specified Point Taylor Polynomials
4.05: Optimisation
4.06: Sketching Graphs
4.07: L'Hopital's Rule and Indeterminate Forms
05: Towards Integral Calculus
5.01: Introduction to Antiderivatives
06: Appendix
6.01: A- High School Material
6.1.01: A.1 Similar Triangles
6.1.02: A.2 Pythagoras
6.1.03: A.3 Trigonometry — Definitions
6.1.04: A.4 Radians, Arcs and Sectors
6.1.05: A.5 Trigonometry — Graphs
6.1.06: A.6 Trigonometry — Special Triangles
6.1.07: A.7 Trigonometry — Simple Identities
6.1.08: A.8 Trigonometry — Add and Subtract Angles
6.1.09: A.9 Inverse Trigonometric Functions
6.1.10: A.10 Areas
6.1.11: A.11 Volumes
6.1.12: A.12 Powers
6.1.13: A.13 Logarithms
6.1.14: A.14 Highschool Material You Should be Able to Derive
6.02: B- Origin of Trig Area and Volume Formulas
6.2.01: B.1 Theorems about Triangles
6.2.02: B.2 Trigonometry
6.2.03: B.3 Inverse Trigonometric Functions
6.2.04: B.4 Cosine and Sine Laws
6.2.05: B.5 Circles, cones and spheres
6.03: C- Root Finding
6.3.01: C.1 Newton's Method
6.3.02: C.2 The Error Behaviour of Newton's Method
6.3.03: C.3 The false position (regula falsi) method
6.3.04: C.4 The secant method
6.3.05: C.5 The Error Behaviour of the Secant Method
6.04: D- Hints for Exercises
6.05: E- Answers to Exercises
6.06: F- Solutions to Exercises