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Notes of Calculus with Analytic Geometry

Calculus

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

At this moment, we are adding notes of Chapter 1, If you wish to add your notes on this page. You can send us at admin [at] mathcity [dot] org.

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

Ch 03: General Theorem, Intermediate Forms

Graphical interpertation of  mean value theorem
  • 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

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ARW Exercise 3.1 Download PDF (1.16 MiB, 5487 downloads) View Online
ARW Exercise 3.2 Download PDF (772.51 KiB, 4769 downloads) View Online
ARW Exercise 3.3 Download PDF (2.59 MiB, 5802 downloads) View Online

Ch 08: Analytic Geometry of Three Dimensions

Cooridnate system
  • 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
  • General quadric surfaces
  • Ruled surfaces
  • Spherical trigonometry
  • The cosine formula
  • The sine formula
  • The four parts (or the cotangent) formula
  • Latitude and longitude
  • Direction of Qibla

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ARW Exercise 8.1 Download PDF (613.14 KiB, 5716 downloads) View Online
ARW Exercise 8.2 Download PDF (1.19 MiB, 5975 downloads) View Online
ARW Exercise 8.3 Download PDF (715.33 KiB, 2284 downloads) View Online
ARW Exercise 8.4 Download PDF (668.08 KiB, 4446 downloads) View Online
ARW Exercise 8.5 Download PDF (321.66 KiB, 2648 downloads) View Online
ARW Exercise 8.6 Download PDF (578.99 KiB, 3260 downloads) View Online
ARW Exercise 8.7 Download PDF (488.29 KiB, 4649 downloads) View Online
ARW Exercise 8.8 Download PDF (105.69 KiB, 4945 downloads) View Online
ARW Exercise 8.9 Download PDF (290.39 KiB, 1451 downloads) View Online
ARW Exercise 8.10 Download PDF (678.58 KiB, 3004 downloads) View Online
ARW Direction of Qibla Download PDF (859.73 KiB, 6161 downloads) View Online

Ch 09: Functions of Several Variables

  • 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

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ARW Exercise 9.1 Download PDF (552.13 KiB, 4225 downloads) View Online
ARW Exercise 9.2 Download PDF (326.7 KiB, 3933 downloads) View Online
ARW Exercise 9.3 Download PDF (363.93 KiB, 3364 downloads) View Online
ARW Exercise 9.4 Download PDF (242.15 KiB, 5398 downloads) View Online
ARW Exercise 9.5 Download PDF (591.9 KiB, 3978 downloads) View Online
ARW Exercise 9.6 Download PDF (975.13 KiB, 5514 downloads) View Online
ARW Exercise 9.7 Download PDF (474.89 KiB, 2630 downloads) View Online
ARW Exercise 9.8 Download PDF (643.65 KiB, 2687 downloads) View Online
ARW Exercise 9.9 NEW Download PDF (509.32 KiB, 2837 downloads) View Online


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