��1��AP΢�e�ֺ��� Introduction of AP Calculus001

1.1�n�̼���ԇThe Courses and Examinations001

1.2AP΢�e��AB��BC��VҪ�� The Examination Outline of AP Calculus AB & BC004

1.3AP΢�e�օ����~�R�� Reference Vocabulary of AP Calculus006

1.4�D��Ӌ������ʹ�� Use of Graphing Calculators013



��2�º��� Functions019

2.1�����Ķ��x Definition of Functions020

2.2�����Ļ������| Function Basic Properties022

2.3�������Ⱥ��� Basic Elementary Functions023

2.4������&�ͺϺ��� Inverse Functions & Composite Functions033

2.5����׃�Q Transforming of Functions035

2.6#��������&�������� Parametric Equations & Vector Functions037

2.7#�O���˺��� Polar Functions039

2.8���} Practice Exercises041



��3�˜O�� Limit043

3.1�O�޵Ķ��x Definition of the Limit044

3.2�O�޴��ڵ��ж� The Limit does Exist or Not045

3.3�O�޵��\�� Operations of Limit047

3.4�O�޵đ��� Applications of Limit052

3.5���} Practice Exercises053



��4���B�m Continuity055

4.1�B�m�ԵĶ��x Definition of the Continuity056

4.2�g���c�ķ�� Kinds of Discontinuities059

4.3�B�m�������� The Continuous Functions Theorem061

4.4���} Practice Exercises063



��5�Œ�����΢�� Derivative and Differential065

5.1�����Ķ��x Definition of the Derivative066

5.2�Ɍ��Ժ��B�m�� Derivability and Continuity072

5.3�����Ļ�����ʽ�ͷ��t Basic Differentiation Formulas and Rules075

5.4�ʽ���t�ͷ������� The Chain Rule & Derivative of an Inverse Function077

5.5�[�����󌧺Ͷ��A���� Implicit Differentiation & Second Derivatives082

5.6#���������� Derivatives of Parametric Equations088

5.7#���������͘O���˺����� Derivatives of Vector Functions and Polar Functions090

5.8΢�� Differential093

5.9���} Practice Exercises096



��6��΢�ֵđ��� Applications of Differential Calculus098

6.1�о����̺ͷ�������Equations of Tangent and Normal099

6.2*ֵ���}The Problems of Maxima and Minima101

6.3�\�ӆ��}The Problems of Motion112

6.4΢����ֵ����The Mean Value Theorem for Derivatives118

6.5����_���tL’Hpital’s Rule120

6.6���㆖�}The Problems of Estimate125

6.7#�W������Euler’s Method129

6.8���}Practice Exercises130



��7�²����e�� The Indefinite Integral132

7.1�����e�ֵĶ��xDefinition of The Indefinite Integral133

7.2�����e�ֹ�ʽFormulas of The Indefinite Integral135

7.3U-��Q��U-Substitution138

7.4#�ֲ��e�ַ�Integration by Parts148

7.5#���������ķe��Integration of Rational Functions153

7.6�����e�ֵđ���Applications of Indefinite Integral156

7.7���}Practice Exercises157



��8�¶��e�� The Definite Integral159

8.1�������c����tRiemann Sums and Trapezoid Rule160

8.2���e�ֵĶ��xDefinition of the Definite Integral165

8.3΢�e�ֻ�������The Fundamental Theorem of Calculus169

8.4���e�ֵ����|Properties of Definite Integral174

8.5�e����ֵ����The Mean Value Theorem for Integrals176

8.6���e�ֵ�Ӌ��The Operations of Definite Integrate178

8.7#�V�x�e��Improper Integrals180

8.8���}Practice Exercises185



��9�·e�ֵđ��� Applications of Integral186

9.1��eArea187

9.2�w�eVolume195

9.3#���L Arc Length204

9.4λ�ƺ;��xDisplacement and Distance206

9.5���} Practice Exercises207



��10��΢�ַ��� Differential Equations209

10.1һ�A΢�ַ���First-Order Differential Equations210

10.2���ɷ��x׃��΢�ַ���Solving Separable D.E.211

10.3б�ʈ� Slope Fields213

10.4ָ�����L�c˥�p Exponential Growth and Decay216

10.5�s�����L�c˥�p Restricted Growth and Decay219

10.6#߉݋˹�B΢�ַ���Logistic Differential Equation222

10.7���} Practice Exercises225



��11�Ÿo�F���� Infinite Series226

11.1���еĘO�� The Limit of The Sequence227

11.2�o�F���� Infinite Series228

11.3�����Ҫ����Four Important Series232

11.4��헼������Ĵ��Єe��Four Tests of Nonnegative Series235

11.5�^���Ք��͗l���Ք� Absolute and Conditional Convergence240

11.6�缉�� Power Series242

11.7̩�ռ��������˄��ּ��� Taylor and Maclaurin Series245

11.8�缉����Ӌ�� Computations with Power Series251

11.9���} Practice Exercises254



���}��Practice Answer255



���Appendix287

A.1���ù�ʽ�Ͷ���Common Formulas and Theorems287

A.2AP΢�e�ֹ�ʽ���YSummary AP Calculus Formula291

A.3VIP���ռ��Wվ298



�����īIReferences299