This course is intended to expose you to the basic ideas of multi-variate Calculus. To be successful, a student must be able at the end of the class to solve the majority of the problems with no external help. All assignments and exams are geared towards and measure how much this goal has been accomplished.

### Specific Learning Objectives

To learn about

- Vector- Valued Functions
- Limits and Continuity of vector-valued functions
- Derivatives of vector-valued functions; Partial and Directional
- Maxima and minima of vector- valued functions
- Lagrange Multipliers
- Differentials
- Curvatures
- Tangent Planes
- Integrals; Double, Triple Integral, Line and Surface Integrals
- Green’s Theorem
- the Divergence Theorem and
- Stoke’s Theorem

### General Learning Objectives

To learn (or at least start learning) how to think mathematically/critically. You will have to

- Memorize and explain definitions, formulas, equations and theorems.
- Learn certain techniques.

Formulas, equations, techniques etc… these are your mathematical tools and as a bare minimum you have to know what they are.

- Learn when certain formulas, equations, techniques etc. can be applied.
- Combine different tools and techniques.
- Identify the correct tools and techniques to deal with unknowns situations.
- Solve problems that look different from what you have seen before.
- Engage in mathematical proofs

Actively participate in this class

- Be present; ask questions; answer questions; take notes.
- Contribute your thoughts.
- Work with other students outside class about this class. Working with a group of other students is highly encouraged, but not during the exams!

It is advisable that you study Calculus 3 with the intend to remember it.

### Core Curriculum Learning Objectives

This course satisfies the core curriculum requirement for Quantitative and Symbolic Reasoning (A3):

An educated person should be able to understand and represent quantitative information symbolically, visually, numerically, and verbally. Communicating information, interpreting data, and

predicting outcomes are important skills in a data-intensive world and require quantitative, symbolic, and statistical reasoning. These types of reasoning, when combined with the ability to identify and apply mathematical techniques to interpret and solve problems enable people to conceptualize ideas and make informed decisions.

Students will be able to:

1: Demonstrate number sense. Estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results. Make appropriate use of technology, being mindful of its limitations when solving problems.

2: Recognize the behavior of polynomial, rational, radical, exponential, and logarithmic models. Represent the quantitative phenomena in these models using verbal, graphical, tabular, and

symbolic form.

3: Solve problems using mathematical (arithmetical, algebraic, geometric, and statistical) methods.

4: Correctly convert, interpret, and analyze different units of measure.

5: Use mathematical models to interpret, hypothesize, and communicate about quantitative phenomena, such as the behavior of drugs in the blood, changes in populations, and fluctuations in prices.