## PHY 220: Calculus With Analytic Geometry II

3 credits | Prerequisites: MAT 104

### Course rationale

This course is a continuation of MAT 104: Calculus and Analytic Geometry. This course emphasizes
integration and integration techniques which are ubiquitous in physics. This further extends to basic vector analysis, which is subsequently applied to the analysis of geometrical objects in multiple dimensions. This course also introduces special functions in mathematical physics which find many applications in different branches in physics.

### Course content

Integral: Antiderivatives and indefinite integrals; Techniques of Integration, Definite Integration, Riemann sums; Properties of Integration, Integration by Reduction, Applications of Integration: area and volume: plane areas, the volume of solids, arc length, and the surface of revolution; Improper Integrals: Gamma and beta functions; Area and Arc Length: Cartesian and polar coordinates; Vectors in plane and space: algebra of vectors, applications in plane and space geometry; Conic Sections: Review of standard forms, reduction of second-degree equations to standard forms, pairs of straight lines, identification of conics, equations of conics in polar coordinates, Infinite Series: Convergence of series

### Course objectives

1. Analyze different aspects of integral calculus.
2. Use the appropriate technique to solve integrals.
3. Apply the techniques learned to evaluate different integrations in physics.
4. Use vector analysis to analyze geometrical objects in two and three dimensions.
5. Analyze different conic sections in proper mathematical formalism.

### References

1. Calculus (9th edition) by James Stewart
2.  Calculus: Early Transcendentals Single Variable (12th edition) by Howard Anton, Irl C. Bivens, and Stephen Davis
3. Calculus (4th edition) by Michael Spivak
4. Calculus (12th edition) by Ron Larson, Bruce H. Edwards