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| 1 | +\chapterimage{orange2.jpg} |
| 2 | +\chapterspaceabove{6.75cm} |
| 3 | +\chapterspacebelow{7.25cm} |
| 4 | +\chapter{Differential Calculus} |
| 5 | + |
| 6 | + \section{Derivative Basics} |
| 7 | + \subsection{Definition of Derivative} |
| 8 | + \subsection{Geometric Meaning of Derivative} |
| 9 | + \subsection{Physical Meaning of Derivative} |
| 10 | + |
| 11 | + \section{Basic Derivative Rules} |
| 12 | + \subsection{Derivatives of Elementary Functions} |
| 13 | + \subsection{Product Rule, Quotient Rule, Chain Rule} |
| 14 | + |
| 15 | + \section{Higher-order Derivatives} |
| 16 | + \subsection{Second-order Derivatives and Applications} |
| 17 | + \subsection{Calculation and Significance of Higher-order Derivatives} |
| 18 | + |
| 19 | + \section{Derivatives of Abnormal Function} |
| 20 | + \subsection{Derivatives of Implicit Functions} |
| 21 | + \subsection{Derivatives of Parametric Equations} |
| 22 | + |
| 23 | + \section{Differentiation} |
| 24 | + |
| 25 | + \section{Related Rates} |
| 26 | + \subsection{Relationships between Rates of Change of Different Quantities} |
| 27 | + |
| 28 | + \section{Taylor Series} |
| 29 | + \subsection{Taylor Expansion of Functions} |
| 30 | + \subsection{Application of Taylor Series} |
| 31 | + |
| 32 | + |
| 33 | + \section{Applications of Differential Calculus} |
| 34 | + \subsection{Tangents and Normals of Curves} |
| 35 | + % \subsection{Analysis of Velocity and Acceleration in Motion} |
| 36 | + \subsection{Mean Value Theorem in Differential Calculus} |
| 37 | + \subsubsection{Fermat's Theorem} |
| 38 | + \subsubsection{Rolle's Theorem} |
| 39 | + \subsubsection{Lagrange's Mean Value Theorem} |
| 40 | + \subsubsection{Cauchy's Mean Value Theorem} |
| 41 | + \subsubsection{Indeterminate Form Limit} |
| 42 | + \subsection{Extrema Problems and Optimization} |
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