Wagner da Rocha

Wagner da Rocha

He/Him

Researcher | Academic | Data Analyst

MA141 – Analytic Geometry and Vectors

Professor of Record, University of Campinas, Institute of Mathematics, Statistics and Scientific Computing, 2025

Course Information - Class D

  • Professor: Wagner Alan Aparecido da Rocha
  • Contact: wdarocha at ime.unicamp.br
  • Schedule: Tuesdays and Thursdays, 08:00–10:00
  • Location: Room CB01
  • Office Hours: Tuesdays, 12:00–13:00
  • Assistant: Rafael Froner Prando
  • Contact: r197034 at dac.unicamp.br
  • Tutor: Maycon Bruno da Silva Santos
  • Contact: m251499 at dac.unicamp.br

Course Overview

Analytic Geometry studies Euclidean geometry through coordinate systems, making it possible to describe geometric phenomena by means of algebraic equations. In addition to formalizing fundamental concepts from linear algebra, the course has direct applications in Physics, Statistics, and Computer Science, among many other fields. For many students, it provides a first encounter with more abstract and formal mathematical structures.

Syllabus

Matrices and linear systems. Vectors and operations. Bases and coordinate systems. Distance, norm, and angle. Dot and cross products. Lines in the plane and in space. Planes. Relative positions, intersections, distances, and angles. Circle and sphere. Polar, cylindrical, and spherical coordinates. Conic sections and classification. Introduction to quadrics.

Textbook

  • Reginaldo J. Santos. Matrizes, Vetores e Geometria Analítica, Imprensa Universitária da UFMG. (free ebook)

Additional References

  • P. Boulos & I. C. Oliveira, Geometria Analítica – Um Tratamento Vetorial, McGraw-Hill, São Paulo, 2nd ed., 2000
  • L. Leithold, O Cálculo com Geometria Analítica, Vol. 1, Harbra, São Paulo, 2nd ed., 1977
  • C. Wexler, Analytic Geometry – A Vector Approach, Addison-Wesley, 1964

Use of References and Materials

There are many excellent books covering the syllabus and content. Students are encouraged to study from their own class notes, the textbook, and any additional material provided by the instructor. The use of online platforms, including AI-powered tools, for solving exercises is strongly discouraged.

Lecture Format

The course will be delivered in person. In exceptional cases, remote lectures may be considered.

Practical Component

Students are expected to practice independently by working through exercises from the textbook and the problem sets. They are encouraged to seek support during office hours and tutoring sessions. Lectures will focus primarily on course content, but may also include time for problem solving and discussion.

Tutoring

This course will be assisted by a PAD tutor (Teaching Support Program) and a PED teaching assistant (Teaching Internship Program). Their scheduled availability is listed below:

\[\begin{array}{|c|c|c|c|c|c|} \hline \textbf{Time} & \textbf{Monday} & \textbf{Tuesday} & \textbf{Wednesday} & \textbf{Thursday} & \textbf{Friday} \\ \hline 12\text{h}-13\text{h} & & \begin{array}{c} \text{Professor} \\ 127\text{ IMECC} \end{array} & \begin{array}{c} \text{PAD} \\ 125\text{ IMECC} \end{array} & & \begin{array}{c} \text{PAD} \\ \text{PB}03 \end{array} \\ \hline 13\text{h}-14\text{h} & \begin{array}{c} \text{PAD} \\ 125\text{ IMECC} \end{array} & \begin{array}{c} \text{PED} \\ \text{PB}13 \end{array} & \begin{array}{c} \text{PAD} \\ 125\text{ IMECC} \end{array} & \begin{array}{c} \text{PED} \\ \text{PB}13 \end{array} & \begin{array}{c} \text{PAD} \\ \text{PB}03 \end{array} \\ \hline 18\text{h}-19\text{h} & \begin{array}{c} \text{PAD} \\ 125\text{ IMECC} \end{array} & \begin{array}{c} \text{PAD} \\ 325\text{ IMECC} \end{array} & \begin{array}{c} \text{PAD} \\ 125\text{ IMECC} \end{array} & \begin{array}{c} \text{PAD} \\ 325\text{ IMECC} \end{array} & \\ \hline \end{array}\]

Practice Exercises

The problem sets available here are suggested for extra practice. They are not graded and do not need to be submitted. However, working through them is highly recommended to reinforce the concepts covered in class.

On this page, you can also find valuable resources to support your ongoing study.

Grading Policy

The course grade will be based on two assignments and one exam. Each assessment will be graded on a scale from \(0\) to \(10\):

  • \(T_1\): First assignment
  • \(T_2\): Second assignment
  • \(P\): Exam

The semester grade \(\text{MS}\) will be computed as:

\[\text{MS} = \max \big\{ 0.2 T_1 + 0.2 T_2 + 0.6 P,\ P \big\}\]

Evaluation criteria:

  • \(\text{MS} \geq 6\): Passed, grade recorded
  • \(2.5 \leq \text{MS} < 6\): Final exam required
  • \(\text{MS} < 2.5\): Failed, grade recorded

If a Final Exam \(\text{EF}\) is required, the final grade \(\text{MF}\) will be computed as:

\[\text{MF} = \dfrac{\text{MS} + \text{EF}}{2}\]

The minimum attendance required is \(\mathbf{75\%}\), corresponding to \(\mathbf{45}\) class hours.

Absences on Assessment Days

Students who miss an assessment due to medical reasons must submit a medical certificate to the instructor within five business days. If accepted, the exam grade may be replaced by the Final Exam grade. In case of absence on the day of an in-class assignment, a replacement activity may be provided at the instructor’s discretion.

Schedule

  • August
    → Tue, 05: Matrices Review – Basic Operations
    → Thu, 07: Matrices Review – Basic Operations
    → Tue, 12: Matrices Review – Linear System and Determinants
    → Thu, 14: Elementary Matrices and Gaussian elimination
    → Tue, 19: Elementary Matrices and Gaussian elimination
    → Thu, 21: Exercises
    → Tue, 26: Graded exercises
    → Thu, 28: Vectors in the plane
  • September
    → Tue, 02: Vectors in \(\mathbb{R}^n\) and the dot product
    → Thu, 04: Orthogonal projection in \(\mathbb{R}^n\) and the cross product in \(\mathbb{R}^3\)
    → Tue, 09: First assignment (\(T_1\))
    → Thu, 11: Discussion of Assignment \(T_1\)
    → Tue, 16: Session with the Teaching Assistant – Exercises
    → Thu, 18: Session with the Teaching Assistant – Exercises
    → Tue, 23: Review for Assignment \(T_1'\)
    → Thu, 25: Second first assignment (\(T_1'\))
    → Tue, 30: Discussion of Assignment \(T_1'\) / Lines in n-Dimensional Space
  • October
    → Thu, 02: Planes in Space
    → Tue, 07: Lines and Planes in Space
    → Thu, 09: Conic Sections
    → Tue, 14: Conic Sections
    → Thu, 16: Second assignment (\(T_2\))
    → Tue, 21: Discussion of Assignment \(T_2\)
    → Thu, 23: Polar Coordinates + Parametric Equations of Conic Sections
    → Tue, 28: No Class – Holiday
    → Thu, 30: Parametric Equations of Conic Sections
  • November
    → Tue, 04: Surfaces and Curves in 3-Space – Quadrics
    → Thu, 06: Surfaces and Curves in 3-Space – Quadrics
    → Tue, 11: Exercises
    → Thu, 13: Surfaces and Curves in 3-Space – Cylindrical Surfaces and Surfaces of Revolution
    → Tue, 18: Surfaces and Curves in 3-Space – Conical Surfaces + Exercises
    → Thu, 20: No Class – Holiday
    → Tue, 25: Exercises
    → Thu, 27: Exam (\(P\))
  • December
    → Tue, 02: No class – Study Week
    → Thu, 04: No class – Study Week
    → Tue, 09: Final Exam (\(\text{EF}\))
  • (If needed) Make-up assessment will be held alongside the Final Exam

Final Remarks

Students requiring learning accommodations due to barriers affecting their academic experience may request specialized support. Unicamp is committed to providing an accessible, equitable, and inclusive academic environment.

For more information, visit:
https://deape.unicamp.br/vida-estudantil/acessibilidade-Pedagogica/paee/
For questions or guidance, contact: paee@unicamp.br