# Entrance Examinations

## Related Pages

All transfer student applicants are required to take Caltech Transfer Entrance Examinations in both mathematics and physics. These exams will be taken after you submit a transfer application to Caltech.

Students must find a faculty proctor at their home institution to administer and submit the exam. After you have asked a faculty member to proctor your exams, you must ask them to fill out the Entrance Examination Proctor Agreement. Once we receive your proctor agreement form, we will email the exams to your proctor.

Each exam takes approximately four hours. **Exams must be returned to Caltech by March 22.**

### Useful Transfer Examination Links

- Sample math and physics exam questions
- Entrance Examination Proctor Agreement Form (coming soon)

### Topics Covered on the Entrance Exams

Not all of these topics may be covered on the exams. This list is intended as a study reference.

**Physics:**
Newtonian mechanics (motion, vectors, trajectories, Newton's laws,
forces), work and energy, energy conservation, momentum, rigid
rotations, angular momentum, harmonic motion, resonance, gravity, Kepler
orbits, ellipses, electric fields and potentials, Gauss's Law, current
resistance, capacitance, inductance, magnetic fields, Faraday's law, AC
and DC circuits, and special relativity

**Math:** Basic
calculus, Taylor polynomials, series, linear algebra (systems of
equations, vectors and matrices, determinants, vector spaces,
transformations, eigenvalues), vector calculus (multiple integrals, line
and path integrals, theorems of Green and Stokes), and differential
equations.

### Sample Math and Physics Textbooks

The following is a list of first- and second-year Caltech math and physics courses and their required textbooks. We recommend using these textbooks as a guide while studying for the exams.

Ma 001A. Calculus of One and Several Variables and Linear Algebra.

- Apostol, Tom; Calculus, Vol. 1. ISBN: 0471000051

Ma 001B (Analytical). Calculus of One and Several Variables and Linear Algebra.

- Apostol, Tom; Calculus, Vol. 2. ISBN: 0471000078

Ma 001b (Practical). Calculus of One and Several Variables and Linear Algebra.

- https://www.math.brown.edu/~treil/papers/LADW/book.pdf

Ma 001C (Analytical). Calculus of One and Several Variables and Linear Algebra.

- Apostol, Tom; Calculus, Vol. 2. ISBN: 0471000078

Ma 001C (Practical). Calculus of One and Several Variables and Linear Algebra.

- Marsden, Jerrold, Tromba, Anthony; Vector Calculus (Sixth), W. H. Freeman, 2012. ISBN: 1429215089

Ma 002A (Analytical). Differential Equations, Probability, and Statistics.

- Robinson, James; An Introduction to Ordinary Differential Equations. ISBN: 0521533910

Ma 002A (Practical). Differential Equations, Probability, and Statistics.

- Boyce, DiPrima; Elementary differential equations and boundary value problems (9), Wiley, 2009. ISBN:0470383348

Ma 002B. Differential Equations, Probability and Statistics.

- Richard J. Larsen, Morris L. Marx; Introduction to Mathematical Statistics and Its Applications. ISBN:0321693949
- Pitman, Jim; Probability. ISBN: 0387979743

Ph 001A. Classical Mechanics and Electromagnetism.

- Steven C. Frautschi et al; The Mechanical Universe: Mechanics and Heat, Advanced Edition (1st paperback), Cambridge UP, 2007. ISBN: 0521715903

Ph 001B (Analytical). Classical Mechanics and Electromagnetism.

- T.M. Helliwell; Special Relativity (1st), University Science Books, 2009. ISBN: 978-1-891389-61-0

Ph 001B (Practical). Classical Mechanics and Electromagnetism.

- Serway, Raymond, Jewett, John; Physics for Scientists and Engineers with Modern Physics (eighth), Brooks/Cole/Cengage, 2010. ISBN: 978-1-4390-4839-9

Ph 001C (Analytic). Classical Mechanics and Electromagnetism.

- Purcell, Edward; Electricity and Magnetism, Berkeley Physics Course Vol. 2 (2nd edition). ISBN: 0070049084

Ph 001C (Practical). Classical Mechanics and Electromagnetism.

- Serway, Raymond,Jewett, John; Physics for Scientists and Engineers with Modern Physics (eighth), Brooks/Cole/Cengage, 2010. ISBN: 978-1-4390-4839-9

Ph 002A. Waves, Quantum Mechanics, and Statistical Physics.

- P. French; Vibration and Waves (1st), W. W. Norton Co., 1971. ISBN: 0393099369
- C. Phillips; Introduction to Quantum Mechanics (Manchester Physics Series), Wiley, 2003. ISBN:0470853247

Ph 002B. Waves, Quantum Mechanics, and Statistical Physics.

- Charles Kittel; Thermal Physics (2nd), W. H. Freeman, 1980. ISBN: 0716710889

Ph 012A. Waves, Quantum Physics, and Statistical Mechanics.

- P. French; Vibration and Waves (1st), W. W. Norton Co., 1971. ISBN: 0393099369
- http://www.people.fas.harvard.edu/~hgeorgi/onenew.pdf

Ph 012B. Waves, Quantum Physics, and Statistical Mechanics.

- David J. Griffiths; Introduction to Quantum Mechanics (2nd), Prentice-Hall, 2004. ISBN: 978-0131118928

Ph 012C. Waves, Quantum Physics, and Statistical Mechanics.

- Charles Kittel; Thermal Physics (2nd), W. H. Freeman, 1980. ISBN: 0716710889