# Notes of Calculus with Analytic Geometry

Notes of the Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore.

Notes of chapter 1 is written by Prof. Muhammad Farooq, notes of chapter 5 is written by Abrar Mustafa and notes of chapter 6 and 7 are written by Mr. Shahid Javed.

We will try our best to add solutions of more chapters as we are able to manage. If you have some notes which you thing are worth to share with other then please contact us from here or email at Admin [at] MathCity [dot] org.

### List of chapters

• Rolle's theorem
• Geometrical interpretation of Rolle's theorem
• The mean vlaue theorem
• Another form of mean value theorem
• Increasing and decreasing functions
• Cauchy's mean value theorem
• Extended mean value theorem
• Indeterminate form
• The form $\frac{0}{0}$
• The form $\frac{\infty}{\infty}$
• The form $0\times \infty$ (or $\infty \times 0$)
• The form $\infty-\infty$
• The forms $0^\infty, 1^\infty, \infty^0$
• Use of expansions

We are very thankful to Muhammad Idrees for providing notes of Exercise 3.3

• Distance between two points
• Point divining a line segment in a given ratio
• Straight line in $\mathbb{R}^3$
• Direction angles of a vector
• Angle between the straight line
• Distance of a point from a line
• Equations for planes
• Angle between two planes
• Straight line as intersection of two planes
• Shortest distance between two straight lines
• Cylindrical coordinates
• Spherical coordinates
• Surfaces
• Surface of revolution
• The cylinder
• Right cylinder
• The cone
• The sphere
• The ellipsoid
• The elliptic paraboloid
• The hyperboloid paraboloid
• The elliptic cone
• Ruled surfaces
• Spherical trigonometry
• The cosine formula
• The sine formula
• The four parts (or the cotangent) formula
• Latitude and longitude
• Direction of Qibla

• Homogeneous Functions
• Differentials
• Change of variables, the chain rule
• Implicit functions
• Directional derivative
• Tangent planes and normal lines
• Extrema of functions of two variables
• Extrema with constraints
• Volume of solid of revolution
• Disc method
• Washer method
• Shell method
• Cross-sectional method
• Area of a surface of revolution
• Volume and area in polar coordinates