You will need
- Textbook, notebook, pen, pencil, ruler, protractor, compass, eraser
Carefully read the prerequisite tasks.
Make the drawing.
Note in the drawing that you are given: lengths of sides, angles. If the condition of the problem says that some segments are equal, put them on the same strokes. Equal angles mark the same handles: single, double, wavy. Corners different quantities highlight different temples.
Explore the figures presented in the task. Remember their definition and properties.
Define a topic that applies to your task. Refresh in the head of the theoretical material on this topic, repeat the main theorem.
Consider the examples of solving problems on this topic. The tasks given in the textbook as examples, often addresses the fundamental issues that you should know.
If you feel confident enough, proceed to the solution of the problem. Start with what you need to find or to prove. Think about how this can be done. That is, solve the problem "from the end".
If you do not see the ways of solving tasks, try to find something using the available data. Perhaps it will come to you idea, how to solve the problem.
Do not get carried away "oral" evidence. Write down the solution of the problem as detailed as possible, unless otherwise specified. Some things may seem obvious to you, but still prescribed them. So you will have practiced the skill, you will better remember the idea.
Advice 2: How to solve the tasks of descriptive geometry
Descriptive geometry is one of the most important subjects in technical universities. It is impossible to become a good engineer, do not learn to solve tasks on descriptive geometry. The ability to read and create drawings, work to editors of computer graphics can be purchased independently, most importantly to some of the most important skills and use them in practice.
You will need
- A textbook on descriptive geometry, the runtime of drawings (AutoCAD or Compass 3D)
Learn to solve tasks on descriptive geometry is possible only with the ability to make plots (figure) according to reports. For this you need to learn how to mark a characteristic point on the additional types. It is also very important to deal with the topic of "intersection of planes". Any plane in the drawing looks like one or more direct.
To mark a characteristic point on the drawing, you need to find the intersection of two planes (in the case of one projection, it'll look like the intersection of the straight lines). For each projection we need to mark all of the characteristic point.
The next step is the connection of characteristic points between them. Usually in problems in descriptive geometry is required to find a characteristic point or to build a third projection on the two known (usually ask to finish the form of "the left"). The most important step when creating a plot is just connecting the dots. For him each point on one of the projections we are signing a letter or a number. Further, after the transfer of the characteristic points on the other two projection sign each transferred point to the corresponding starting point of the symbol. Then we connect the dots between the additional projections as they were connected in a given projection.
For the successful solution of problems in engineering graphics and descriptive geometry, it is desirable to study topics such as "Body rotation" and "cross Sections of bodies with planes". This will allow you to avoid mistakes when connecting the characteristic points.
For the solution of problems by descriptive geometry it is convenient to use environment for 3D modeling. One of the most convenient and intuitive for beginners (which is important) is the medium Compass. It is possible, having two projections, to the third in automatic mode.
Advice 3: How to solve problems in theoretical mechanics
Theoretical mechanics is one of the most fundamental scientific disciplines that plays a major role in preparing future engineers and technicians. The task of "teormeh" is based on the knowledge of higher mathematics and physics.
Consider the first stage of studying theoretical mechanics — statics. For the solution of problems in theoretical mechanics in this section it is necessary to know the basics of vector algebra and be able to perform most actions on vectors in two-dimensional and three-dimensional space. Knowing the basics of coordinate system, especially a Cartesian rectangular system, would be of great help in solving some problems "termeh". To understand the challenges and confidently find a solution, it is necessary to combine this knowledge with the performance quality of the drawing at the specified conditions.
Learn such parts of higher mathematics as analytic geometry, differential calculus of functions of one variable, as well as the basics of differential geometry, in particular, the concept of the accompanying triangular. This information will be useful when solving problems in theoretical mechanics from the course kinematics. Not the last for this section is the development of imagination, as you must be able to present different development process.
Solve problems from section dynamics using knowledge on computation of integrals, partial derivatives and integration of simple differential equations of first and second order.
Train yourself to solve problems in theoretical mechanics for the simplest examples. For example, the most popular among students of the problem books on this topic is a book authored by A. A. Yablonski. It can take in the University library or downloaded from any Internet source. Scan the highlights when solving problems.
Start the solution of problems in theoretical mechanics with an analysis of the conditions. Take a sheet of paper and draw on it the specified schema. Indicate all forces that act on the body. Make a equation and determine the values using all of the above knowledge.
Advice 4: How to learn to solve problems in geometry
Geometry is one of the most important areas of mathematics. The ability to solve mathematical tasks required in exams in mathematics at school and University, and many professions in practice. How to acquire this skill?
Possession of theoretical material will give you the tools, without which it is impossible, even simple tasks. The science of geometry is divided into two sections - a planimetry and solid geometry. Need to have basic knowledge in both disciplines.
For the solution of the macroscopic (planar) problems need to know the formula to determine areas and perimeters of shapes: parallelograms (including their varieties: diamonds, rectangles), trapezoids, triangles, circles. Learn the theorems on the equality and similarity of triangles - they will be needed for most planimetric tasks. It is also necessary to know definitions of angles, parallel and perpendicular lines.
Learn the theory needed to solve stereometric problems (associated with large-volume bodies in space). Formula calculate volume and surface area of a parallelepiped, pyramid, cone, sphere and cylinder, not only will become a faithful assistant in solving geometry problems; this knowledge will help you in everyday life - in the repair, construction, arrangement of the interior.
To consolidate knowledge and enhance understanding of the formulas will help the substitution of the trial values of the parameters (sides, radius) studied geometric figures. By setting the values of the sides of a square 10 cm, one can compute its perimeter and area formulas P = 4 * a and S = a * a. Not only will you get the results (40 cm and 100 sq cm. respectively), but also gain experience of calculations of operating and geometric parameters. With it, you will be able to solve simple tasks.
The solution to complex problems is not without preliminary evidence of the equality of shapes. The division of polygons and composite figures direct the conduct of the perpendiculars (altitudes) and medians will help to break complex objects into more simple elements, to calculate areas and volumes which will not be easy.