# Math 121 Problems, Solutions, Handouts

• Warnings [ pdf ]
• Tables of Formulae [ pdf ]
• Tables of integrals you should know or be able to derive quickly [ pdf ]

### Notes

• A Careful Area Computation [ pdf ]
• The Definition of the Integral [ pdf ]
• Substitution [ pdf ]
• Substitution Examples [ pdf ]
• Cylindrical Shells Example [ pdf ]
• Approximating a Function Near a Specified Point (error in integral form) [ pdf ]
• Trig Substitutions [ pdf ]
• Integrating sec x and sec3 x [ pdf ]
• Torque [ pdf ]
• Centroid Example [ pdf ]
• Partial Fractions Examples [ pdf ]
• Roots of Polynomials [ pdf ]
• The Partial Fractions Decomposition [ pdf ]
• The Form of Partial Fractions Decompositions [ pdf ]
• Complex Numbers and Exponentials [ pdf ]
• Simple Numerical Integrators - Derivation [ pdf ]
• Simple Numerical Integrators - Error Behaviour [ pdf ] (updated March 10, 2003)
• Simple Numerical Integrators - Determining Step Size [ pdf ] (updated March 10, 2003)
• Error Formulae for Taylor Polynomials [ pdf ]
• Computation of Pi. [ pdf ]

### More Notes

• Trig Functions [ pdf ]
• The Cosine Law and Addition Formulae [ pdf ]
• Approximating a Function Near a Specified Point (error in mean value theorem form) [ pdf ]
• The RC Circuit [ pdf ]
• The RLC Circuit [ pdf , applet ]
• Spreadsheet implementation of Simpson's Rule [ pdf ]
• Linear Regression [ pdf ]
• Richardson Extrapolation and Romberg Integration [ pdf ]
• Simple ODE Solvers - Derivation [ pdf ]
• Simple ODE Solvers - Error Behaviour [ pdf ]
• Simple ODE Solvers - Variable Step Size Methods [ pdf ]
• Error Control for the Polar Area Formula [ pdf ]