Topic | Dates |

Sequences and convergence, Basic techniques for computing limits. Boundedness. Monotone convergence. Telescoping series. Geometric and harmonic series. Alternating series. Absolute convergence. Comparison and limit comparison tests. Ratio test. Root test. Integral test. p-test. Power series. Taylor and Maclaurin series. | Jan 8 thru Feb 5 |

Review of vector geometry. Dot and cross products. Parametric curves. Velocity. Tangent vectors. Arclength. Vector integrals. Arclength parameterization. Acceleration. Normal and binormal. Curvature formulas. Osculating circle. Components of acceleration. Ellipse. Archimedean spiral. The fundamental equations for plane curves. Torsion. Frenet-Serret equations. Torsion formula. | Feb 7 thru Feb 23 |

Reading week, no classes. | Mar 5 thru Mar 9 |

Multivariate functions. Limits. Continuity. Partial derivatives. Directional derivatives. Gradient. Chain rule. Higher order derivatives. Extremals and their classification. The Hessian. Lagrange multipliers. | Feb 26 thru Mar 19 |

Easter break, no classes. | Mar 30 and Apr 2 |

Double integrals. Fubini's theorem. Change of coordinates. Variable substitution. Polar coordinates. Surface area. Triple integrals, cylindrical and spherical coordinates. | Mar 21 thru Apr 9 |

Revision. | Apr 11 thru Apr 16 |

**Important dates** | |

Written quiz. | TBA |

Add/drop deadline. | Jan 23 |

Withdrawal deadline. | Mar 13 |