# Calc 3 Final Review Essay

## Test Reviews

Test reviews are conducted for several mathematics courses and other courses throughout the term by Teaching Center tutors. The reviews are typically scheduled two nights prior to the examination. Review materials may also be published on the Teaching Center website. To view materials on this page, you must have a PDF viewer such as Adobe Acrobat Reader.

### Chemistry 1025 Test Reviews

Review Materials | Review Time | Location | Old Tests |
---|---|---|---|

Test 1 – 1/26/18 | Review Packet | 1/24/18 5-7pm | FLG 245 |

Test 2 – 2/14/18 | Review Packet | 2/12/18 5-7pm | CSE E220 |

Test 3 – 3/29/18 | 3/27/18 5-7pm | TUR 2333 | |

Test 4 – 4/19/18 | 4/17/18 5-7pm | TUR 2333 | |

Final – 4/30/18 | 4/29/18 5-7pm |

### Chemistry 2045 Test Reviews

Review Materials | Review Time | Location | Old Tests |
---|---|---|---|

Test 1 | Review Packet | 1/30/18 5-7pm | WM 100 |

Test 2 | Review Packet | 3/12/18 5-7pm | MAT 18 |

Test 3 | 4/8/18 5-7pm | MAT 18 | |

Final | 4/29/18 5-7pm |

### Physics 2048 Test Reviews

Review Materials | Review Time | Location | Old Tests |
---|---|---|---|

Test 1 – 2/15/18 | Review Packet | 2/14/18 5:10-7:00pm | NPB 1001 |

Test 2- 3/29/18 | 3/27/18 6:30-8:30pm | PUGH 170 | |

Final – 5/1/18 | 4/30/18 5-7pm |

### Mathematics Test Reviews (scroll down)

You must **print mathematics review materials** and **bring them with you** to the review.

You may pickup a paper copy of an old test for free at the Teaching Center. If we run out of paper copies for a particular test, **only then** will we post a scanned copy of the old test in the table below. Old exams are available for math classes up to Calc 2.

**Answers** to the old tests are posted in the Math Study Center located in Southeast Broward Hall, except for Calc II, which is posted in the Tutoring Center Lobby in Southwest Broward Hall.

See the table below for times and locations of reviews:

### MAC1105–College Algebra

Review Materials | Review Date & Time | Location | Old Tests | |

Test 1 – 2/1/18 | Review Packet | 1/31/18 6-8pm | FLG 220 | Test 1 |

Test 2 – 3/1/18 | Review Packet | 2/28/18 6-8pm | FLG 220 | |

Test 3 – 4/5/18 | 4/4/18 6-8pm | MCCA G186 | ||

Test 4 – 4/24/18 | 4/23/18 6-8pm | FAB 105 | ||

Final – 4/28/18 | 4/27/18 4-6pm |

### MAC1140–Pre-Calculus / Algebra

Review Materials | Review Date & Time | Location | Old Tests |
---|---|---|---|

Test 1 – 2/6/18 | Review Packet | 2/5/18 6-8pm | FLG 220 |

Test 2 – 3/15/18 | Review Packet Additional Problems | 3/13/18 6-8pm | WEIM 1064 |

Test 3 – 4/12/18 | 4/11/18 6-8pm | FLG 220 | |

Final – 4/28/18 | 4/26/18 4-6pm |

### MAC1147–Precalculus / Trig

Review Materials | Review Date & Time | Location | Old Tests |
---|---|---|---|

Test 1 – 1/30/18 | Review Packet Additional Problems | 1/29/18 5:30-7:30pm | FLG 210 |

Test 2 – 2/22/18 | Review Packet Additional Problems | 2/20/18 5:30-7:30pm | FLG 280 |

Test 3 – 3/26/18 | 3/25/18 5-7pm | TUR L007 | |

Test 4 – 4/16/18 | 4/15/18 5-7pm | TUR L007 | |

Final – 4/28/18 | 4/26/18 4-6pm |

### MAC2233–Survey of Calculus 1

Review Materials | Review Date & Time | Location | Old Tests |
---|---|---|---|

Test 1 – 2/13/18 | Review | 2/12/18 5:30-7:30pm | FLG 210 |

Test 2 – 3/20/18 | 3/19/18 5:30-7:30pm | MCCC 100 | |

Test 3 – 4/12/18 | 4/10/18 5:30-7:30pm | NRN 0137 | |

Final – 4/28/18 | 4/26/18 4-6pm |

### MAC2234–Survey of Calculus 2

Review Materials | Review Date & Time | Location | Old Tests | |
---|---|---|---|---|

Test 1 – 2/6/18 | Review Packet | 2/5/18 5-7pm | FAB 105 | Exam 1 |

Test 2 – 3/15/18 | Review Packet | 3/13/18 5-7pm | FAB 105 | Test 2 |

Test 3 – 4/5/18 | 4/3/18 5-7pm | FAB 105 | ||

Final – 4/28/18 | 4/27/18 4-6pm |

### MAC2311–Calculus 1

### MAC2312–Calculus 2

Review Materials | Review Date & Time | Location | Old Tests |
---|---|---|---|

Test 1 – 2/13/18 | Review Packet Additional Review Problems | 2/12/18 5-7pm | NEB 202 |

Test 2 – 3/13/18 | Review Packet | 3/12/18 5-7pm | NRN 0137 |

Test 3 – 4/12/18 | 4/10/18 5-7pm | WEIM 1064 | |

Final – 4/28/18 | 4/26/18 4-6pm |

### MAC2313–Calculus 3

Review Materials | Review Date & Time | Location | Old Tests |
---|---|---|---|

Test 1 – 2/1/18 | Review Packet | 1/30/18 5-7pm | WEIM 1064 |

Test 2 – 3/1/18 | Review Packet | 2/27/18 5-7pm | FAB 105 |

Test 3 – 4/5/18 | 4/3/18 5-7pm | WEIM 1064 | |

Final – 4/28/18 | 4/27/18 4-6pm |

### MGF1106–Math for Liberal Arts and Sciences

** This course covers Calculus of several variables. The concepts are extensions of the concepts from Calculus I. It is necessary to remind the students of those basic concepts, as the course progresses. Multivariable Calculus is an important tool in Science and Engineering. The instructor should emphasize the importance of all relevant concepts, including: curves and surfaces in Euclidean 3-space, length and curvature, area and volume; surfaces, partial derivatives, total differential, tangent planes to surfaces; gradient; vector-valued functions; path integral; Stokes' theorem, which should be stated, with an emphasis on its important particular cases, Green's Theorem and Divergence Theorem - followed by a few basic examples. **

**Grading Policy**

**Homework is worth 20% of the final grade. However in order to pass the class your overall grade in the HW at the end of the semester should be at least 50%. This may appear radical, but besides the exams, the HW system is a major tool the instructor has to asses your class performances. The instructor will check regularly your HW score and let you know if you are not on track. Examinations: **

Exam #1: Wed, February 11, 5:30-6:30 | room Math110 | worth 15% of the final grade |

Exam #2: Wed, March 11, 5:30-6:30 | room Math110 | worth 20% of the final grade |

Exam #3: Wed, April 22, 5:30-6:30 | room Math110 | worth 20% of the final grade |

Final Exam: Mon, May 11, 10:30-1:00 | worth 30% of the final grade |

Overall grade: a perfect score in all tests and homeworks results in a overall grade of 105% .

If your overall score is less than 60% you will receive an F grade, in between 60-69% you will receive a D grade, in between 70-79% you will receive a C grade, in between 80-89% you will receive a B grade, in between 90-99% you will receive an A grade, with 100% or more you will receive A+.

Overall grade: a perfect score in all tests and homeworks results in a overall grade of 105% .

If your overall score is less than 60% you will receive an F grade, in between 60-69% you will receive a D grade, in between 70-79% you will receive a C grade, in between 80-89% you will receive a B grade, in between 90-99% you will receive an A grade, with 100% or more you will receive A+.

**Exam Policy**

** Students are expected to take the midterm exams and the final exam as scheduled. Students who live close enough to Lubbock (75 miles around Lubbock) will have to take the midterm exams and final exam at Texas Tech University in Lubbock at the Mathematics and Statistics department. If students have a conflict in schedule or are far away from Lubbock, they need to provide necessary documentation, and arrange a different place and/or time for examination. In that cased, depending on their geographic location, each student should make arrangements with a certified testing service. In case no agreeable solution can be found, the Texas Tech University Testing Services in Lubbock will be designated to administer the examination. Testing centers (including the TTU Testing Center) charge a fee to administer the exam. **

**The following link can be used to obtain a copy of the proctor form in***Adobe Acrobat***(.pdf) format****Proctor form PDF File**** **

** This is a distance class, all the students enrolled in this class should be highly responsible in managing their schedule. This course moves very fast. If you fall behind, even by one section, you may not be able to catch up, since each section generally depends very heavily on the ones before. A student enrolled in this class has to be capable to read and understand the textbook. If in the past you struggled in self-lecturing mathematics, then this is not the class for you and it is highly recommended you switch to a face-to-face class. The instructor expects for the student to read each section of the textbook, watch the videos and read the class-notes before attempting to solve the homework problems. When asking for help you need to show all your work, by typing it on the email (better) or by attaching a scanned copy of your work. When asking for help for a WebWork problem it is recommended you use the button email to the instructor at the bottom of the screen, otherwise you may not get any answer. **

Videos

Review of Sections 9.1-9.4

** Vector Basics**** **

** Vector Component Form**** **

** Scalar Multiplication **** **

** Adding and Subtracting Vectors**** **

** Vector Operations - Example 1 **** **

** Standard Unit Vectors **** **

** Magnitude of a Vector **** **

** Magnitude of a Vector - Example 1 **** **

** Unit Vector **** **

** How to Normalize a Vector **** **

** 3D Vectors **** **

** Vector Dot Product **** **

** Dot Product - Example 1 **** **

** Using Dot Product to Find the Angle Between Two Vectors **** **

** Finding Angles Using Dot Products - Example 1 **** **

** Vector Projections **** **

** Vector Projections - Example 1 **** **

** Vector Cross Product **** **

** Vector Cross Product - Example 1 **** **

** Vector Cross Product - Extra Theory **** **

Section 9.5

** Parametric Equations **** **

** Graphing Parametric Equations **** **

** Eliminating the Parameter **** **

** Eliminating the Parameter - Example 1 **** **

** Differences in the Parametrization **** **

** How to Parametrize a Curve **** **

** Parametrization - Example 1 **** **

** Lines in Space **** **

** Lines in Space - Example 1**** **

** Lines in Space - Example 2**** **

** Lines in Space - Symmetric Equations **** **

** Lines in Space - Parametric to Symmetric **** **

**Lines in Space - Symmetric to Parametric**** **

**Lines in Space - Are These Lines Parallel?**** **

Section 9.6

**Equations of Planes in Space**** **

**Plane in Space - Extra Theory**** **

**Standard vs General Form of a Plane**** **

**Normal Vector of a Plane**** **

**Equation of a Plane - Example 1**** **

**Equation of a Plane - Example 2**** **

**Equation of a Plane - Example 3**** **

**Distance Between a Point and a Plane**** **

**Distance Between a Point and a Plane - Example 1**** **

**Distance Between a Point and a Line**** **

**Distance Between a Point and a Line - Example 1**** **

** Angle Between Two Planes **** **

** Angle Between Two Planes - Example 1 **** **

** Line of Intersection of Two Planes **** **

Section 9.7

**The Equation of the Sphere**** **

**Introduction to Quadric Surfaces**** **

** Quadric Surface: The Ellipsoid **** **

** Quadric Surface: The Hyperboloid of Two Sheets **** **

** Quadric Surface: The Hyperboloid of One Sheets **** **

** Quadric Surface: The Elliptical Cone **** **

** Quadric Surface: The Elliptical Paraboloid **** **

**Quadric Surface: The Hyperbolic Paraboloid **** **

Section 10.1

**Introduction to Vector Valued Functions**** **

**The Domain of a Vector Valued Function**** **

**Determine a Vector Valued Function from the Intersection of Two Surfaces**** **

**Limits of Vector Valued Functions**** **

Section 10.2

**The Derivative of a Vector Valued Function**** **

** Properties of the Derivatives of Vector Valued Functions**** **

** The Derivative of the Cross Product of Two Vector Valued Functions **** **

** Determining Where a Space Curve is Smooth from a Vector Valued Function **** **

** Determining Velocity, Speed, and Acceleration Using a Vector Valued Function **** **

** Indefinite Integration of Vector Valued Functions **** **

** Ex: Integrate a Vector Valued Function **** **

** Indefinite Integration of Vector Valued Functions with Initial Conditions **** **

** Ex: Find the Velocity and Position Vector Functions Given the Acceleration Vector Function **** **

Section 10.4

** Determining the Unit Tangent Vector **** **

** Ex: Find a Unit Tangent Vector to a Space Curve Given by a Vector Valued Function **** **

** Determining the Unit Normal Vector **** **

** Arc Length Using Parametric Equations **** **

** Determining Arc Length of a Curve Defined by a Vector Valued Function **** **

** Ex: Determine Arc Length of a Helix Given by a Vector Valued Function **** **

** Determining Curvature of a Curve Defined by a Vector Valued Function **** **

Lecture Notes from Spring 2014

**Lecture Notes for sections 9.1-9.5 **** **

**Lecture Notes for section 9.6 **** **

**Lecture Notes for sections 9.7 and 10.1 **** **

**Lecture Notes for section 10.2 **** **

**Lecture Notes for section 10.4 **** **

** Exam 1 is scheduled in room Math110, Mathematics Building on Wednesday February 11 at 5:30 pm. Exam 1 is comprehensive of Sections 9.5-9.7, 10.1, 10.2, 10.4 (HW02 and HW03). However to be prepared for the exam all the material reviewed in sections 9.1-9.4 (HW01) is necessary. To prepare for the exam review all 40 problems in HW02 and HW03. You need to know how to solve each of them without the use of the book, formula sheets and/or calculator. The exams consists of 6 questions and should be completed in 50 mins. A sample of how the exam is structured is given below. You need to bring with you a pencil, an eraser and student ID. A blank page at the end of the test is provided for scratch work, and other will be available if needed. **

**Exam 1 Solution Key **** **

Videos

Sections 11.1-11.3

** Introduction to Functions of Two Variables **** **

** Level Curves of Functions of Two Variables **** **

** Limits of Functions of Two Variables **** **

** First Order Partial Derivatives **** **

** Implicit Differentiation of Functions of One Variable Using Partial Derivatives **** **

** Second Order Partial Derivatives **** **

Sections 11.4-11.6

** Differentials of Functions of Two Variables **** **

** Applications of Differentials of Functions of Several Variables **** **

** The Chain Rule for Functions of Two Variable with One Independent Variable **** **

** Ex: Chain Rule - Function of Two Variables with One Independent Variable **** **

** Partial Implicit Differentiation **** **

** The Chain Rule for Functions of Two Variable with Two Independent Variables **** **

** Ex: Chain Rule - Function of Two Variables with Two Independent Variable **** **

** Ex: Chain Rule - Function of Two Variables with Three Independent Variable **** **

** Directional Derivatives **** **

** Ex: Find a Value of a Directional Derivative - f(x,y)=ln(x^2+y^2) **** **

** The Gradient **** **

** Ex: Find the Gradient of the Function f(x,y)=xy **** **

** Ex: Use the Gradient to Find the Maximum Rate of Increase of f(x,y)=(4y^5)/x from a Point **** **

** Determining a Unit Normal Vector to a Surface **** **

** Verifying the Equation of a Tangent Plane to a Surface **** **

** Determining the Equation of a Tangent Plane **** **

** Ex 1: Find the Equation of a Tangent Plane to a Surface **** **

** Ex 2: Find the Equation of a Tangent Plane to a Surface (Exponential) **** **

Sections 11.7 and 11.8

** Determining the Relative Extrema of a Function of Two Variables **** **

** Applications of Extrema of Functions of Two Variables I **** **

** Applications of Extrema of Functions of Two Variables II **** **

** Applications of Extrema of Functions of Two Variables III **** **

** Absolute Extrema of Functions of Two Variables **** **

** Lagrange Multipliers - Part 1 **** **

** Lagrange Multipliers - Part 2 **** **

** Maximize a Function of Two Variable Under a Constraint Using Lagrange Multipliers **** **

Lecture Notes from Spring 2014

**Lecture Notes for sections 11.1 **** **

**Lecture Notes for section 11.2-11.3**** **

**Lecture Notes for sections 11.4 **** **

**Lecture Notes for section 11.5 and 11.6 **** **

**Lecture Notes for section 11.6 and 11.7 **** **

**Lecture Notes for section 11.7 **** **

**Lecture Notes for section 11.8 **** **

** Exam 2 is scheduled in room Math110, Mathematics Building on Wednesday March 11 at 5:30 pm. Exam 2 is comprehensive of Sections 11.2-11.8 (HW04, HW05 and HW06). To prepare for the exam review all 50 problems in the homeworks. You need to know how to solve each of them without the use of the book, formula sheets and/or calculator. The exams consists of 6 questions and should be completed in 50 mins. A sample of how the exam is structured is given below. You need to bring with you a pencil, an eraser and student ID. A blank page at the end of the test is provided for scratch work, and other will be available if needed. **

**Exam 2 Solution Key **** **

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