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Notes of Calculus with Analytic Geometry

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Calculus with Analytic Geometry by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore-Pakistan is one of the books studied widely in Bachelor and undergraduate classes. There are total of ten chapters. We try our best to get the notes and solutions of this book written by different authors so that teachers and students can get better understanding of the different notion in mathematics and work hard to learn basic concepts.

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

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

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

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, 9382 downloads) View Online
ARW Exercise 8.2 Download PDF (1.19 MiB, 7327 downloads) View Online
ARW Exercise 8.3 Download PDF (715.33 KiB, 39335 downloads) View Online
ARW Exercise 8.4 Download PDF (668.08 KiB, 36259 downloads) View Online
ARW Exercise 8.5 Download PDF (321.66 KiB, 2213 downloads) View Online
ARW Exercise 8.6 Download PDF (578.99 KiB, 25146 downloads) View Online
ARW Exercise 8.7 Download PDF (488.29 KiB, 25664 downloads) View Online
ARW Exercise 8.8 Download PDF (105.69 KiB, 15646 downloads) View Online
ARW Exercise 8.9 Download PDF (290.39 KiB, 6495 downloads) View Online
ARW Exercise 8.10 Download PDF (678.58 KiB, 9365 downloads) View Online
ARW Direction of Qibla Download PDF (859.73 KiB, 37607 downloads) View Online
  • 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, 40392 downloads) View Online
ARW Exercise 9.2 Download PDF (326.7 KiB, 28743 downloads) View Online
ARW Exercise 9.3 Download PDF (363.93 KiB, 31423 downloads) View Online
ARW Exercise 9.4 Download PDF (242.15 KiB, 22047 downloads) View Online
ARW Exercise 9.5 Download PDF (591.9 KiB, 11315 downloads) View Online
ARW Exercise 9.6 Download PDF (975.13 KiB, 13158 downloads) View Online
ARW Exercise 9.7 Download PDF (474.89 KiB, 23063 downloads) View Online
ARW Exercise 9.8 Download PDF (643.65 KiB, 23025 downloads) View Online
ARW Exercise 9.9 NEW Download PDF (509.32 KiB, 22256 downloads) View Online

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