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A Course of Calculus by A. N. Das (published by NCBA),
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1. Two-Dimensional (2D) Analytical Geometry
- Coordinate Transformations: Covers translation and rotation of axes, as well as orthogonal transformations to simplify equations.
- General Equation of Second Degree: Classification of conic sections into parabolas, ellipses, or hyperbolas using invariants.
- Properties of Conics: Finding the center, axes, asymptotes, eccentricity, foci, tangents, normals, and polar equations of conics.
- Pairs of Straight Lines: Homogeneous second-degree equations and conditions under which they represent intersecting or parallel lines.
2. Three-Dimensional (3D) Analytical Geometry
- Lines and Planes: Coordinates in 3D space, direction cosines, direction ratios, finding angles, and intersections between lines and planes.
- Spheres: General equations of a sphere, plane sections of a sphere, intersections of two spheres, and tangent planes.
- Cones and Cylinders: Equations of right circular cones, enveloping cones, quadratic cones, and cylinders.
- Central Conicoids: Foundations of central quadric surfaces such as ellipsoids, paraboloids, and hyperboloids.
3. Vector Algebra and Analysis
- Vector Basics: Multiplication, components of vectors, collinearity, and coplanarity conditions.
- Vector Products: Scalar (dot) product, vector (cross) product, scalar triple product, and vector triple product.
- Applications: Using vector equations to describe geometric lines, planes, and computing lengths/distances in 3D space.
- Vector Fields: Intro to gradient, divergence, and curl operations.
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