Differential Calculus: An Introduction to Analysis (Part II)

• Leverages the concept of derivatives to analyze rates of change in higher dimensions.
• Applications in physics (e.g., acceleration as the second derivative of position) and engineering (e.g., curvature in design).
• Includes Leibniz’s theorem for computing nth-order derivatives.

5. Tangents and Normals (Polar & Parametric Forms)

• Equation of tangent and normal in Cartesian, parametric, and polar coordinates
• Subtangent and subnormal
• Angle between two curves.

Interesting fact from the book’s problem sets:
The evolute of a parabola ( y^2 = 4ax ) is a semicubical parabola ( 27ay^2 = 4(x-2a)^3 ). The evolute has a cusp – a sharp point where the center of curvature jumps. This cusp is physically where a caustic forms in a parabolic mirror.

3. Second-Hand Scans (Gray Area)

• Some university WhatsApp or Telegram groups share scanned copies made by seniors. While common, these are technically unauthorized. If you receive such a file, consider it a temporary aid and buy the print copy later to support the authors.