About this course
This is a two-semester, calculus-based introductory physics course at first-year university level. It covers the same ground as the standard first-year texts (Halliday, Resnick and Walker, Fundamentals of Physics; Young and Freedman, University Physics; Serway and Jewett, Physics for Scientists and Engineers). Its problem-solving style draws on H. C. Verma, Concepts of Physics, Volumes 1 and 2. A chapter-by-chapter map to these books is in the References at the end.
Prerequisites. You should know school algebra and trigonometry. You should also be taking, or have taken, a first course in single-variable calculus (derivatives and simple integrals). The calculus tools you need are introduced in Chapter 1 as you go.
How each chapter is organised.
- Concepts, built up step by step. Each section develops one idea from the ground up.
- Worked examples between the sections. Every example has a complete solution: the physical reasoning, a labelled diagram or setup, the equations, the algebra, the numbers and a check of the answer.
- Key-idea, definition and common-mistake boxes. These pick out what to remember and what to avoid.
- A chapter summary collecting the main results.
- Practice problems in three levels:
- Level A, concept check: short questions that test whether you understood the ideas.
- Level B, standard problems: typical homework and exam questions.
- Level C, challenge problems: multi-step questions in the spirit of H. C. Verma’s harder exercises.
Full step-by-step solutions to every practice problem are in the separate Solutions Manual. Try each problem seriously before you look at the solution.
Conventions. We use SI units throughout and take \(g = 9.8\ \text{m/s}^2\) unless a problem says otherwise. Vectors are written \(\vec{A}\), unit vectors \(\hat{\imath}, \hat{\jmath}, \hat{k}\), and magnitudes \(A = |\vec{A}|\).
Semester 1: Mechanics, Waves and Thermal Physics
| Week | Chapter | Topics |
|---|---|---|
| 1 | 1. Measurement, Units, Dimensions, Vectors | SI units, dimensional analysis, significant figures, vector algebra, dot and cross products |
| 2–3 | 2. Kinematics | Position, velocity, acceleration, motion graphs, constant acceleration, projectiles, relative motion |
| 3–4 | 3. Newton’s Laws | Forces, free-body diagrams, inertial frames, pseudo-forces, connected bodies, pulleys |
| 5 | 4. Friction and Circular Motion | Static and kinetic friction, inclines, uniform and non-uniform circular motion, banking |
| 6 | 5. Work, Energy and Power | Work by variable forces, kinetic energy, potential energy, conservation of energy, power |
| 7 | 6. Centre of Mass, Momentum, Collisions | Centre of mass, impulse, conservation of momentum, elastic and inelastic collisions, variable mass |
| 8 | Midterm examination | Chapters 1–6 |
| 9–10 | 7. Rotational Motion | Rotational kinematics, torque, moment of inertia, angular momentum, rolling |
| 10 | 8. Gravitation | Newton’s law of gravitation, field and potential, orbits, escape speed, Kepler’s laws |
| 11 | 9. Simple Harmonic Motion | SHM equation, energy, springs, pendulums, damped and forced oscillations |
| 12 | 10. Elasticity and Fluids | Stress, strain, moduli, pressure, Pascal, Archimedes, continuity, Bernoulli, viscosity |
| 13 | 11. Waves and Sound | Travelling waves, superposition, standing waves, sound, beats, Doppler effect |
| 14 | 12. Heat and Thermodynamics | Temperature, calorimetry, kinetic theory, first law, processes, heat engines, second law |
| 15 | Final examination | Chapters 1–12 |
Semester 2: Electricity, Magnetism, Optics and Modern Physics
| Week | Chapter | Topics |
|---|---|---|
| 1 | 13. Electric Charge and Field | Charge, Coulomb’s law, electric field, continuous distributions, dipoles |
| 2 | 14. Gauss’s Law | Electric flux, Gauss’s law, symmetric charge distributions, conductors |
| 3 | 15. Electric Potential | Potential energy, potential, equipotentials, field from potential |
| 4 | 16. Capacitance and Dielectrics | Capacitors, series and parallel, energy storage, dielectrics |
| 5–6 | 17. Current and DC Circuits | Current, resistance, Ohm’s law, EMF, Kirchhoff’s rules, RC circuits, meters |
| 7 | 18. Magnetic Field and Forces | Lorentz force, charged particle motion, force on currents, torque on loops |
| 8 | Midterm examination | Chapters 13–18 |
| 9 | 19. Sources of Magnetic Field | Biot–Savart law, Ampère’s law, solenoids, magnetic materials |
| 10 | 20. Electromagnetic Induction | Faraday’s and Lenz’s laws, motional EMF, inductance, RL circuits, energy in B |
| 11 | 21. AC Circuits and EM Waves | Phasors, reactance, LCR resonance, power factor, displacement current, EM waves |
| 12 | 22. Geometrical Optics | Reflection, refraction, total internal reflection, mirrors, lenses, optical instruments |
| 13 | 23. Wave Optics | Huygens’ principle, Young’s double slit, thin films, single-slit diffraction, gratings, polarisation |
| 14 | 24. Photons, Atoms and Nuclei | Photoelectric effect, de Broglie waves, Bohr atom, X-rays, nuclear structure, radioactivity |
| 15 | Final examination | Chapters 13–24 |
Suggested assessment
| Component | Weight |
|---|---|
| Weekly problem sets (drawn from Levels B and C) | 20% |
| Laboratory work | 15% |
| Midterm examination | 25% |
| Final examination | 40% |
A problem-solving strategy
Every worked example in these notes follows the same four steps. Make them a habit.
- Identify. What is being asked? Which physical principles apply (Newton’s laws, energy conservation, Gauss’s law, …)? What are the knowns and unknowns?
- Set up. Draw a diagram. Choose axes and a sign convention. Draw a free-body diagram where forces are involved. Write the governing equations symbolically.
- Execute. Solve the equations algebraically first. Substitute numbers, with units, only at the end.
- Evaluate. Check the units and dimensions. Ask whether the magnitude is reasonable. Check limiting cases (what happens if \(m \to 0\), \(\theta \to 90^\circ\), …?).